Calc multiple choice

If f'(x)=(x-a)(x-b)(x-c) and a<b<c, then which of the following could be the graph at f(x)? B

B

If y=x3√x and t=3-ln(x) then dy/dt= A) -4/3x^(4/3) B) -4/3x^(-2/3) C) -3/4x^(3/4) D) 4/3x^(4/3)

A) -4/3x^(4/3)

The average value of the function f(x)=e^-xsinx on the closed interval [1,π] is A) 0.129 B) 0.145 C) 0.155 D) 0.276

A) 0.129

Let f be the function given by f(x)=x^2lnx. For what value of x is the slope of the line tangent to the graph of f at (x,f(x)) equal to 2? A) 1.305 B) 1.548 C) 2.548 D) 4.773

A) 1.305

∫(sex^2x)(tan^2x)dx= A) 1/3tan^3x+c B) tan^3x+c C) 1/3sec^3x+c D) tan^2x+c

A) 1/3tan^3x+c

The table above gives values of a function y and its derivative at selected values of x. if dv/dt is continuous on [1,5], what is the value of ∫(2 to 5)(dy/dx)dx? A) 46 B) 49 C) 63 D) 72

A) 46

If f is a differentiable function on the closed interval [a,b] which of the following theorems fully apply to function f? A) I and II only B) I and III only C) I, II, and III D) none of the above

A) I and II only

Suppose that f(x) is a twice differentiable function on the closed interval [a,b]. If there is a number c, a<c<b, for which f'(c)=0, which of the following must be true? A) None B) I only C) II only D) III only

A) None

∫(e to e^2) (dx)/(xlnx)= A) ln2 B) 1/2 C) 3/2 D) 2

A) ln2

What is an equation of the line tangent to the graph of f(x)=7x-x^2 at the point where f'(x)=3? A) y=3x+4 B) y=3x+8 C) y=3x-10 D) y=3x-16

A) y=3x+4

Let f and g be functions that are differentiable for all real numbers x with g(x)=f(x)/x. If y=2x-3 is an equation of the line tangent to the graph of f at x=1, what is the equation of the line tangent to the graph of g at x=1? A) y=3x-4 B) y=x-2 C) y=3x-2 D) y=2x-3

A) y=3x-4

(slope field) B

B

The current price of a compact car is $14,500. The price of a compact car is changing at a rate of 120+180√t dollars per year. What will be the approximate price of a compact car five years from now? A) $15,300 B) $16,440 C) $18,120 D) $22,600

B) $16,440

∫x√(x^2+1)dx A) (3/4)(x^2+1)^(3/2)+C B) (1/3)(x^2+1)^(3/2)+C C) (2/3)(x^2+1)^(3/2)+C D) (1/3)x^2(x^2+1)^(3/2)

B) (1/3)(x^2+1)^(3/2)+C

The area of the region in the first quadrant enclosed by the y-axis and the graphs of y=3cosx and y=x is A) 1.683 B) 2.078 C) 3.447 D) 7.005

B) 2.078

(table) The function f is continuous on the closed interval [1,10] and has the values shown in the table above. Using the intervals [1,3], [3,7], [7,8], and [8,10], what is the approximation on ∫(1 to 100)(f(x))dx obtained from a right Riemann sum? A) 6 B) 7 C) 13 D) 23

B) 7

Function f is differentiable and decreasing for all real numbers. If y-f(2x^3-3x^2), for which of rthe following intervals of x will the value of y NOT be decreasing? A) (-∞,0] and [1,∞) B) [0,1] only C) (-∞,0] only D) [1,∞) only

B) [0,1] only

let f'(x)=((2-x)^2)/X^3 for x>0. If x is always positive and f(1)=2, what is the equation for f? A) f(x)=1/2+4/x-5/(2x^2) B) f(x)=ln(x)+4/2-2/x^2 C) f(x)=ln(x)+1/x^4-4/3x^3+7/3 D) f(x)=ln(x)-2/x^2+4/x+2

B) f(x)=ln(x)+4/2-2/x^2

How many points of inflection does the graph of y=2x^6+9x^5+10x^4-x+2 have? A) one B) two C) three D) four

B) two

if f is the function defined by f(x)=((2x+3)(3-x))/(2x-1)^2, the graph of f will have a horizontal asymptote at which of the following equations? A) y=-3/2 B) y=-1/2 C) y=1/2 D) y=1

B) y=-1/2

Let f be a differentiable function for all x. Which of the following must be true? A)II only B)III only C)I and III only D)II and III only

B)III only

Let f(x) be a differentiable function defined only on the interval -2≤x≤10. The table below gives the value of f(x) and it's derivative f'(x) at several points of the domain. (table) A) (0,22) B) (0,28) C) (0,31) D) (0,36)

C) (0,31)

If sin(xy)=x^2, then dy/dx= A) 2xsec(xy) B) 2xsec(xy)-y C) (2xsec(xy)-y)/x D) (2xsec(xy))/y

C) (2xsec(xy)-y)/x

The amount of a radioactive substance decreased according to the equation dy/dt=ky where k is a constant and time t, is measured in days. If half of the present amount of the substance will decrease in 20 days, what is the value of k? A) -6.021 B) -0.693 C) -0.035 D) -0.015

C) -0.035

The mass, m(t) in grams, of a tumor t weeks after it begins growing is given by m(t)=te^7/800. What is the average rate of change, in grams per week during the fifth week of growth? A) 0.341 B) 0.619 C) 0.655 D) 1.113

C) 0.655

lim(h->0)((2(x+h)^5-5(x-h)^3-2x^5+5x^3)/(h)) 9s A) 0 B) 10x^4+15x^2 C) 10x^4-15x^2 D) -10x^4+15x^2

C) 10x^4-15x^2

what is the 20th derivative of y=cos(2x)? A) -2^20cos(2x) B) -2^20sin(2x) C) 2^20cos(2x) D) 2^20sin(2x)

C) 2^20cos(2x)

what is the maximum value of the first derivative of f(x)=3x^2-x^3 A) 0 B) 2 C) 3 D) 4

C) 3

Let f be the function defined by f(x)=ln(3x+2)^k for some positive constant k. If f'(2)=3, what is the value of k? A) ln8 B) 4 C) 8 D) 16

C) 8

The graph of a function f whose domain is the closed interval [1,7] is shown above. (piecewise graph) Which of the following statements about f(x) if true? A) lim(x->3)(f(x))=f(1) B) lim(x->4)(f(x))=f(5) C) lim(x->5)(f(x))=f(4) D) lin(x->6)(f(x))=f(3)

C) lim(x->5)(f(x))=f(4)

A sugar ant crawls along the vertical edge of a cereal box with a velocity is given by v(t)=2^-t+(t-2)^2+(t-2)^3-(t-2)^4+2, for 0≤t≤3. For what intervals is the speed of the sugar ant decreasing? A) (0, 0,776) only B) (0.77, 1.501) and (2.075, 3) C) (0, 0.776) and (1.474, 2.103) D) (0, 0.776) and (1.501, 2.074)

D) (0, 0.776) and (1.501, 2.074)

If f(x)=x^(-1/3), what is the derivative of the inverse of f(x)? A) -1/3x^(-4/3) B) 1/3x^(-2/3) C) -3x^-2 D) -3x^-4

D) -3x^-4

if ∫(2 to 8)(f(x)dx=-10 and ∫(2 to 4)(f(x)dx=6, then ∫(8 to 4)(f(x))dx= A) -16 B) -4 C) 4 D) 16

D) 16

A tank is being filled with water at the rate of 300√t gallons per hour with t>0 measured in hours. If the tank is originally empty, how many gallons of water are in the tank after 4 hours? A) 600 B) 900 C) 1200 D) 1600

D) 1600

if y=(2x^2+10^4, then dy/dx= A) 4(2x^2+1)^3 B) 4x92x^2+1)^3 C) 16(2x^2+1)^3 D) 16x(2x^2+1)^3

D) 16x(2x^2+1)^3

A region R enclosed but he coordinate axes and the graph of y=h(x-5)^2, k>0. When this region is revolved around the x-axis, the solid formed has a volume of 2500π cubic units. What is the value of k? A) 2√15 B) 4 C) √5 D) 2

D) 2

The base of a solid is the region enclosed by the graph of y=3(x-2)^2 and the coordinate axes. If every cross section perpendicular to the x-axis is a square, then the volume of the solid is A) 19.2 B) 24.0 C) 25.6 D) 57.6

D) 57.6

The figure above shows the graph of y=f(t). Let g(x)=g(0)+ ∫ (0 to x)f(t)dt. If g(-3)=2, what is the value of g(0)? A) -8 B) -6 C) 6 D) 8

D) 8

The volume of a cube is increasing at a rate of 20 cubic centimeters per second. How fast, in square centimeters per second, is the surface areas of the cube increasing at the instant when each edge of the cube is 10 centimeters long? A) 2 B) 4 C) 6 D) 8

D) 8

Let f(x) be a continuous function and let A be the area of the shaded region in the figure above. Which of the following must be true? A) I only B) I and II only C) I and III only D) I, II and III

D) I, II and III

Let f(x) be a differentiable function defined for all real numbers. The table below gives the value of f(x) and its derivative f'(x) for selected values of x. A) I and II only B) I and III only C) II and III only D) I, II, and III

D) I, II, and III

The expression 4 ∫(0 to 2)p(x)dx gives the number of people living on one side of a 4 mile-long stretch of highway, where x is the number of miles from the highway. What are the units of p(x)? A) people B) square miles C) people per mile D) people per square mile

D) people per square mile

A particle moves along the x-axis so that its position at any time t>0 is given by x(t)=t^3+22t+3-6cos(πt). For what value of t, if any, is the velocity negative? A) t=1/2 B) t=1 C) t=3/2 D) the velocity is never negative

D) the velocity is never negative

if f(x)= {(x^2+2 for x≤1, 2x for x > 1 then f'(1) is A) 1 B) 2 C) 3 D) undefined

D) undefined

if (dy/dx=2xy, then (d^2y)/(dx^2)= A)2x+2y B)4x^2y C)2x^2y+2y D)4x^2y+2y

D)4x^2y+2y