AP Calc 2017 mc

if f(x)= (5-x)/(x^2+2), then f'(x)=

2x^7-15x^2-2/(x^2+2)^2

f(x)=-3+6x^2-2x^3... largest open interval both concave up and increasing?

(0,1)

if f is the function given by f(x) 3x^2-x^3, then the average rate of change of f on the closed interval [1,5] is

-13

if f(x)=sin(x^2+pi), then f'(sq root of 2pi)=

-2sq root of 2pi

w(t)=25-t^2 for 0<t<5, what is the rate of change at t=3?

-6

if f(x)= lnx, the lim as x->3, f(x)-f(?)/c-3 is

1/3

∫(1/3x+12)dx

1/3ln|x+4|+C

dy/dz=ky, k is a constant, at t=0 population is 120g, inc at a rate of 24 grams per day... expression for y(t)?

120e^y/5

t 0 0.5 2 3 v(t) 20 60 40 30 using the trapezoidal sum...

130

if f(x)= (2x^2+5)^7, then f'(x)=

28x(2x^2+5)^6

if x^2+xy-3y=3, then at point (2,1) dy/dx

5

0∫2(x^3+1)^(1/2)x^2dx

52/9

if n∫-10 g(x)dx=-3 and n∫6 g(x)dx=5, then -10∫6 g(x)dx=

8

The function f has a first derivative given by f'(x)=x^4-6x^2-8x-3. In what intervals is the graph of f concave up?

A) (2,infinity) only

the region enclosed by the graphs y=x^2 and y=2x is the base of a solid. For the solid, each cross section perpendicular to the y-axis is a rectangle with hight 3 times the base in the xy plane. which gives the volume?

A) 3 0∫4 (sq root of y- y/2)^2dy

let f be a continuous function for all real numbers. Let g be g(x)= ∫f(t)dt. If the average rate of change of g on 2<x<5 is 6, which is true?

A) the average value of f of 2<x<5 is 6

the graph of which of the following functions has exactly one horizontal asymptote and no vertical asymptotes?

A) y=1/x^2+1

A file is downloaded to a computer at a rate modeled by the differentiable function f(t), when t is time in seconds since the start of the download and f(t) is measured in megabits per second. Which of the following is the best interpretation of f'(5)=2.8?

B) At time t=5 seconds, the rate at which the file is downloaded to the computer is increasing at a rate of 2.8 megabits per second

x 1 2 3 4 5 f(x) 9 4 0 -3 -5 If f is twice differentiable on the interval 1<x<5 which is true?

B) f' is negative and increasing for 1<x<5

The function g is continuous of the closed interval [1,4] with g(1)=5 and g(4)=8. Which guarantees there is a number C in the open interval (1,4) where g'(c)=1?

B) g is differentiable on the open interval (1,4)

Let H(x) be an antiderivative of (x^3+ sinx)/(x^2+2). If H(5)=pi, then H(2)=?

B)-5.867

an isosceles right triangle with legs of length s has a=1/2s^2. At the S= sq root of 32 centimeters, the area is increasing at a rate of 12 sq cm per sec. At what rate is the length of the hypotenuse of the triangle increasing in cm per sec?

B)3

for a certain continuous function f, the RRS approximation of 0∫2 f(x)dx with n subintervals of equal length is 2(n+1)(3n+2)/n^2 for all n. What is the value of 0∫2f(x)dx

B)6

let f be the function f(x)= ln(x^2+1), let g be g(x)= (x^5+x^3). The line tangent to the graph of f at x=2 is parallel to the line tangent to the graph of g at x=a, where a is a positive constant. What is a?

C) 0.447

let f be a function with derivative given by f'(x)=(x^3-8x^2+3)/(x^3+1) for -1<x<9. At what value of x does f attain a relative max?

C) 0.638

The continuous function f is positive and has domain x>0. If the asymptotes of the graph of f are x=), y=2. What is true?

C) Lim as x->0 f(x)= infinity and f(x)=2

lim as x-> infinity ln(e^3x)+x))/x=

C)3

If the average value of a continuous function f on the interval [-2,4] is 12, what is -2∫4 f(x)/8dx?

C)9

f''(x)=x(x-1)^2 (x+2)^3 g''(x)=x(x-1)^2 (x+2)^3+1 h"(x)= x(x-1)^2 (x+2)^3-1 The twice differentiable functions f,g,h have second derivatives given above. What functions have a graph with 2 points of inflection?

C)f and g only

the number of bacteria in a container increases at the rate of r(t) bacteria per hour. If there are 1000 bacteria at time t=0, which gives the number of bacteria at t=3 hours?

D) 1000+ 0∫3 R(t)dt

A particle travels along a straight line with velocity v(t)= (3e^(-t/2))sin(2t) mps. what is the total distance in meters, traveled by the particle during the time 0<t<2?

D) 2.261

The graph of a differentiable function f is shown. Which is true?

D) f'(3)<f'(0)<f'(-2)

for any function f, which statement is true?

II and III only (if f is continuous at x=a, then lim as x->a f(x)=F(a), f is differentiable at x=a, then lim as x->a f(x)= f(a))

f(x)=x-2/z|x-2| ... what is true?

f has a jump discontinuity at x=2

f(x)=2cosx+1, approximation for f(1.5) by the line tangent to f at x=pi/2?

pi-2

moves along x axis time t>0, position is x(t)=12e^t(sint), first time which velocity of particle is 0?

pi/4

if f is the function given by f(x)=e^10/3, which is the following is an equation of the line tangent to the graph of f at the point (3ln4, 4)

y-4= 4/3(x-3(ln4))

what is a solution for dy/dx=2y/2x+1 with condition y(0)=e for x>-1/2

y=2ex+e