ap calc with calculator

first derivative is f'(x)=ln(x^4-2x^2+1)+1 on the interval [-2,2]. which of the following represent all when concave up>

(-1,0) and (1,2]

let f be a function whose first derivative is f'(x)=ln(x^4-2x^2+1)+1 on the interval [-2,2]. which of the following represents all the intervals on which f is concave up?

(1,0) and (1,2]

given f(x)=x^5-5x^4+15x+10 what are all the points of inflection of f(x)

(3,-107)

the graph of f(x)=e^sin(x)-2 crosses the x axis at one point on the interval [0,1]. the slope of f(x) at this point is

1.442

if f'(x)=sin(x^2+3)-x^3+4x, then f has a local minimum for what values of x?

-0.035

water is exiting a giant cone shaped funnel at a rate of 15 cubic inches per second. the funnel is 75 inches high and has a maximum radius of 40 inches, what is the rate at which the water level of the funnel is changing when the water is 15 inches high?

-15/64pi in/sec

f(x)=(x-3)^4. to identify the correct values for each missing part in the table. what do you believe that f'(2) rounded to 3 decimal places is?

-1=-15, -0.1=-4.641, -0.01=-4.060, 0.01=-3.940, 0.1=-3.439, 1=-1.0 check 2.1 version 5 -4.000

limit as x->-infinity 12x^4-4x/17x^3-7x^4

-2

a weight resting on a spring is compressed 6 units down from its resting position s=0 and released at time t=0. the function that describes its position is x(t)=-6 cos t. what is its acceleration at time t=10?

-5.03

Limit as x-> infinity sin|x|-3+x-4x^3/x+3-^2x-|x|

-infinity

Limit as x-> infinity ln(3x^2/7x^3-10)

-infinity

limit as x->-infinity x^7-300x^4+x^3-2

-infinity

limit as x->-infinity 6x^2+5x^3-|x|/cos x-3+4x^5+2x

0

limit as x->0- e^3/x

0

air is pumped into a balloon at a rate of 50 cm^3/min. find the rate at which the rate which the radius of the ballon is increasing when the radius of the ballon is 10 cm. assume that the balloon is a sphere,

0.040cm/min

the Egyptians built a square pyramid that was 480 feet high and 88,000,00 cubic feet in volume. each block that was used was 4 cubic feet in volume and they placed 288 of these blocks per day in order to build their pyramid. when the pyramid reached a height of 400 feet, what was the rate at which the height was increasing per day. v=88,000,000-160w^2+w^2h/3

0.0754 ft/day

a spherical balloon is increasing in volume at a rate of 30 cm^3/min. at what rate is the radius increasing when the balloon has a volume of 80picm^3

0.156cm/min

a particle moves along the x-axis and its position in feet at any time t>1 sec is described by the function f(x)=sin^-1(-1/t). what is its velocity at 5/3 sec?

0.45 ft/sec

the position of a block attached to a horizontal spring is represented by the following equation s(t)=4sin(5^1/2t) in the interval t=[0,1], when is the bock at rest?

0.702 seconds

what is the slope of the function f(x)=sin^2x at x=pi/4

1

limit as x->3 x^2+3x-18/x^2+2x-15

1.125

A soda company is trying to cut down on material costs for their drinks. Their drinks hold 14 in.³ of liquid (approximately 8 ounces) and come in the shape of a cylinder. What is the radius that will give the least amount of surface area for the drink containers? Use the volume and surface area formulas of a cylinder.

1.306in

limit as x->1 x^2+6x-7/x^2+4x-5

1.333

let d(t) be the distance in miles a train has traveled in t hours. what is the velocity equation for a train whose distance equation is represented by the following equation: d(t)=t^1/2-3lnt+4t

1/(2t^1/2)-3/t+4

bocky rolboa finishes his morning jog strong by sprinting up the steps to the entrance of a national monument at 20ft/sec. if the steps are angled 30 degrees above the horizontal, what is the rate at which his elevation is increasing?

10 ft/sec

for what value of c will the function be continuous? -4x+c x<1 x^3-1x+7 x>1

11

a bungee jumper leaps off a bridge 80 feet above the ground using a 55-foot long bungee cord. her height as a function of time: h(t)=60 sin(t+1)/(t+1)^3/4+30 how far does the bungee cord stretch during the initial descent?

14 feet

for what value of c will the function be continuous? -4x+c x<5 x^3-1x+5 x>5

145

An aquatic wildlife company is making an open, rectangular fish tank. The volume required for the fish tank is 80 cubic feet. The bottom of the fish tank must be made of sheet metal, but the sides are made of glass. Two opposite sides of the fish tank must be square. What is the minimum cost to make a fish tank with these requirements if glass is $2.00 per square foot and sheet metal is $1.50 per square foot? Round to the nearest cent.

173.55

a soccer player is standing in the center of a soccer field of professional size (105m, 68m). there is a spectator on one side at the midfield line. the player kicks the ball directly into the center of the goal, and the ball travels at a constant speed of 23 m/s. how fast is the distance between the ball and the spectator changing when it reaches the edge of the field and enters the goal?

19.305

as shown in the above picture, a 6 foot tall man is standing on a beach at night. he watches as a boat out at sea sails away fro him at a constant rate of 10 feet per minute. the boat has a powerful light shining back at him, casting a shadow. if the light is 28 feet above the water, at what rate is the length of the man's shadow changing in feet per minute?

2.727 ft/min

limit as x-> infinity 4x^2-3x+1/6x+x-4

2/3

a cylindrical container with a diameter of 6 cm and a height of 20 cm is being filled with water at a rate of 6cm^3/sec. what is the rate at which the water level is rising in the container?

2/3pi cm/sec

for what value of c will the function be continuous? -4x+c x<2 x^2x+8 x>2

20

babe ruth stands at home plat. when babe ruth had sprinted 45 feet, and had reached a speed of 23 feet per second, his teammate had sprinted 35 feet toward second base, and the distance between them was decreases at a rate of 5 feet per second. how fast his teammate was running at that point?

21.427 ft/sec

Given that f(x)= -2x+c x<6 x^3-x+7 x>6 what value of c will the function be continuous?

229

the side length of a cube are all increasing at a constant rate of 2inches/hour. what is the rate of change of the volume with respect to time when the volume is 8in^3

24 in^3/hr

a bungee jumper leaps off a bride 80 feet above the ground using a 55-foot-long bungee cord. her height as a function of time is modeled by the following equation: h(t)=60sin(t+1)/(t+1)^3/4+30

29.6ft/s

a man is walking away from a street light. the street light is 18 feet tall and the man is 6 feet tall. if the man is walking in a straight line away from the street light at a constant rate of 4 feet/second, what is the rate at which his shadow is lengthening?

2ft/sec

the radius of a circle is increasing. at a certain instant, the rate of increase of the area of the circle is three times the rate of increase at its circumference. what is the radius of the circle at that instant?

3

Given f(x)=3|x+2|-5, use the definition of the derivative to find f'(3) find f'(-2)

3 DNE

A company is seeking to maximize its profits. It finds that its cost function is C(x)=2x^3−12x^2+27x−5 where x is the number of units sold in thousands. If the company charges $9 for each unit, what is the number of units they should sell in order to maximize their profit?

3000 units

-4x+c x<5 x^2-2x+4 x>5 what value of c will the function be continuous?

39

find dy/dx y=(ln(x)+x^2)^4

4(ln(x)+x^2)^3(1/x+2x)

a 13 foot ladder is sliding down a wall at a rate of 2 feet/sec. what is the rate at which the bottom of the ladder is moving away from the wall when the top of the ladder is 12 feet high on the wall

4.8 ft/sec

a bungee jumper leaps off a bridge 80 feet above the ground using a 55-foot long bungee cord. her height as a function of time: h(t)=60 sin(t+1)/(t+1)^3/4+30 what is the highest elevation the bungee jumper achieves after the initial descent?

43 feet

the position in feet of a particle is given: x(t)=t^3-4t^2+6 at what time t>0 will the velocity of the particle reach 35 feet per second?

5 seconds

the bacteria Imawesomitis sofrigincoolia was being grown in the science laboratory. After a few studies, researchers found that the population was quadrupling(multiplying by 4) every hour! they started with 6 and counted how many there were after every hour that passed. After how many hours will the pop grow at a rate of approx. 34,070 specimens per hour?

6.0 hours

a kit is rising into the air at 8 ft/sec. the man holding the kite is a horizontal distance of 50 feet away from the kite. when the kite reaches a height of 70 ft, what is the rate at which the line is being released?

6.510 ft/sec

A company wants to minimize their average cost per unit. They know that their total cost for x number of units produced is C(x)=x^3−12x^2+68x where x is measured in hundreds. How many should they produce in order to minimize their average cost per unit? Note that the average cost is C(x)/x.

600 units

an automated, swinging security light, hanging from the corner of a 35 ft tall building, is lighting the ground in front of the building. the angle 0 is increasing at a rate of 0.6 radians per minute when the light on the group is 50 ft away from the edge of the building. at the instant, what is the speed at which the light on the ground is traveling?

63.857 ft/min

A company does some market research and finds that the price they can charge is dependent on the number of units they sell. The company finds that B(x)=−1/2x+30 where x is the number of units sold in hundreds and B is the price. If the total cost of producing x number of units is C(x)=2x^2−15x+42, how much should the company produce so that they can maximize their profit? Note that P(x)=R(x)−C(x) and R(x)=x*B(x) where P is the profit, R is the revenue, and C is the cost.

900 units

given that f'(x) to the left of x=4 is negative f'(x) to the right of x=4 is positive f'(x)=0 what is true about f(4)

f(4) is a local minimum

which of the following derivatives is false?

all are true 3.1 version 7

for what values of x is the function f(x)=(|x^2-100|)^1/2 continuous and differentiable?

all real numbers except x=-10 and x=10

where does the sign of the concavity of the function f(x)=x^3-3/4x change?

at x=1.44

describe the concavity of the curve described by 2x^2-y^2=y-x+1 at the point (3,4)

concave down

given f(x)=|x|^1/2, describe the concavity of f(x)

concave down for all x, except x=0

d^44/dx^44(cosx), the 44th derivative of cos(x)

cosx

let f be the function defined by f(x)=(|x+3|)^1/2 which of the following statements is true?

f is not differentiable at x=-3

if f(x)=x^2e^(1/x) find f'(x)

f'(x)=e^(1/x)(2x-1)

A box manufacturing company would like to minimize the amount of material it takes to make their boxes. The boxes have widths of 10 cm and do not have any tops. Given that the volume of the box is 110 cm³, identify the length L and height H that will minimize the surface area. Round to three decimal places.

height:2.345cm lengh:4.690cm

Limit as x-> infinity ln(10x^2+5/4x)

infinity

limit as x->-5- x/x+5

infinity

limit as x->-7- x/x+7

infinity

limit as x-> infinity ln(3x/2x-10)

ln(3/2)

if a function has a smooth maximum at x=4 (it's not a cusp or corner), its second derivative at

negative

in the interval [0,pi], where does the slope of the function f(x)=cotx equal -4/3

pi/3

researchers are studying the movement of two different particles. the position in feet of particle A at any given time T is described by the function f(t)=tan^-1(t-1) and the position of particle v at g(t)=-cot^-1(2t). at what time are the speeds of these two particles equal?

t=0.58

the position of a particle moving along the x-axis is modeled by x(t)=ln(t^2)+t^2. when is the particle's velocity equal to 5?

t=1/2 and 2

the function x(t)=at-bt^2 models the position of a particle on the x-axis at time t. for what values of t is the particle at rest?

t=a/2b

which statement best describes the function displayed below? upside down u

the function is concave down and there are no points of inflection

at which x-values are the inflection points of the function located?

the zeros

the table above shows values of f' for selected values of x. given that f(x) is continuous, which of the following statements must be true of f?

version 2 f has at least 2 points of inflection

Mrs. Jones always wanted a white picket fence in front of her house. Mr. Jones, her husband, wants a fence around the entire house including a decently-sized lawn in the front and a garden in the back. The fence border should look like a rectangle (see picture above). He calculated that he would need to fence off an area of 4,000 square feet in order to fit all these things. He wants to appease his wife and at least build the white picket fence in front of the house. He plans to build the rest of the fence with chain link, a cheaper material. Given that a white picket fence costs $7 per foot and a chain link fence costs $4 per foot, what dimensions for the entire area will give the cheapest cost for the entire fence? Round your answers to the nearest whole number.

width:54 ft height:74 ft

for which value of x does f(x) have a local maximum?

x=-2 when positive to negative

given that f is a continuous function on the interval [-5,4], at what values of x does f have a local minimum?

x=4 x=-5 version 3

find the positive x-value for the function f(x)=15cot^-1(1/3x) where f'(x)=-1

x=6

what is the equation fo the line tangent to the function f(x)=3 tan x+x/cos(x)-6 at x=0

y=4x-6