Packet 2 ap calc

B) (-2,3)

76) The graph of f', the derivative of f, is shown above for -2<x<5. On what intervals is f increasing?

C) I and II only

77) The figure above shows the graph of a function f with domain 0<x<4. Which of the following statements are true?

B) 1<x< 1.691

78) the first derivative of the function f is defined by f'(x)= sin(x^3-x) for 0<x<2. On what intervals is f increasing?

B) -13

79) If integration from -5 to 2 of f(x) dx=-17 and integration from 5 to 3 of f(x)dx=-4, what is the value of integration from -5 to 5 f(x)dx?

E) five

80) The derivative of the function f is given by f'(x)= x^2cos(x^2). How many points of inflection does the graph of f have on the open interval (-2,2)

E) -7 + integration from 2 to 7 of f(t) dt

81) If G(x) is an intermediate for f(x) and G(2)=-7, then G(4)

C) 0.055

82) A particle moves along a straight line with velocity given by v(t)= 7-(1.01)^-t^2 at time t>0. What is the acceleration of the particle at time t=3

B) 11.833

83) What is the area enclosed byy the curves y=x^3 -8x^2+ 18x- 5 and y=x+5

C) 4 only

84) The graph of the derivative of a function f is shown in the figure above. The graph has horizontal lines at x=-1, x=1, and x=3. At which of the following values of x does f have a rel max

B) -2.25

85) The table above gives values of a function f and its derivative at selectd values of x. If f' is continuous on the interval (-4,-1), what is the value of integration from -4 to -1 f'(x) dx

C

86) The table gives selected values of the velocity, v(t), of a particle moving along the x-axis. At time t=0, the particle is at the origin. Which of the following could be the graph of the position, x(t), of the particle for 0<t<4

D) 6.512

87) An object traveling in a straight line has position x(t) at time t. If the initial position is x(0)=2 and the velocity of the object is v(t)= (1+t^2)^1/3, what is the position of the object at time t=3

C) -48pi

88) The radius of a sphere is decreasing at a rate of 2 cm/sec. At the instant when the radius of the sphere is 3cm, what is the rate pf change, in square cm/sec, of the surface area of the sphere?

E) For some k, where -2<k<2, f'(k) does not exist

89) The function f is continuous for -2<x<2 and f(-2)=f(2)=0. If there is no c, where -2<c<2, for which f'(c)=0, which of the following statements must be true?

A

90) the function f is continuous on the closed interval (2,4) and twice differentiable on the open interval (2,4). If f'(3)=2 and f"(x)<0 on the open interval (2,4), which of the following could be a table of values for f?

C) 0.183

91) What is the average value of y=cos x/x^2+x+2 on the closed interval (-1,3)

B) 7 integration from 0 to 4 of f(x) dx

92) A city located beside a river has a rectangular boundary as shown in the figure above. The population density of the city at any point along a strip x miles from the river's edge is f(x) persons per square mile. Which of the following expressions gives the population of the city?

A) 0<t<2

A particle moves along a straight line. the graph of the particles position x(t) at time t is show above for 0<t<6. The graph has horizontal tangents at t=1 and t=5 and a point of inflection at t=2. For what values of t is the velocity of the particle increasing?

B) 6

A particle moves along the x-axis with velocity given by v(t)= 3t^2+6t for time t>0. If the particle is at position x=2 and t=0, what is the position of the particle at t=1

B) db/dt= kp(N-p)

A rumor spreads among a population N people at a rate proportional to the product of the number of people who have heard the rumor and the number of people who have not heard the rumor. If p denotes the number of people who have heard the rumor, which of the following differential equations could be used to model this situation with respect to time t, where k is a positive constant?

D) (x^2+2)^2(7x^2-6x+2)

If f(x)=(x-1)(x^2+2)^3, then f'(x)=

E) -3(3^1/2)/2

If f(x)=cos(3x), then f'(pi/9)

D) -2/x^2 e^(2/x)

If f(x)=e^(2/x), then f'(x)=

A) 2lnx+2/x

If f(x)=x^2+2x, then d/dx(f(lnx))=

D) 1-ycos(xy)/ xcos(xy)

If sin(xy)=x, then dy/dx =

A) -3

In the xy-plane, the line x+y=k, where k is a constant, is tangent to the graph of y=x^2+3x+1. What is the value of k?

A) -1/2

Let f be a differentiable function such that f(3)=15, f(6)=3, f'(3)=-8, and f'(6)=-2. The function g is differentiable and g(x)=f^-1(x) for all x. what is the value of g'(3).

D) 3 and 6 only

Let f be a function with a second derivative given by f"(x)=x^2(x-3)(x-6). What are the coordinates of the points of inflection of the graph f?

C) dy/dx= xy + x

Shown above is a slope field for which of the following differential equations

B) 0.6

The function f is twice differentiable with f(2)=1, f'(2)=4, and f"(2)=3. What is the value of the approximation of f(1.9) using the line tangent to the graph of f at x=2

B

The graph of a function f is shown above. Which of the following could be teh graph of f', the derivative of f?

C) Right Riemann sum approximation of integration from 1 to 3 f(x) dx with 4 subintervals of equal lengths

The graph of the function f is shown above for 0<x<3. Of the following, which has the least value?

C) 2 and 5 only

The graph of the function f shown above has horizontal tangents at x=2 and x=5. Let g be the function defined g(x)= integration from 0 to x of f(t)dt. For what values of x does the graph of g have a point of inflection

D) g(1)

The graph of the piecewise function f is shown in the figure above. If g(x)= integration -2 to x of f(t)dt, which of the following values is greatest

E) The graph of f changes concavity in the interval (0,2)

The polynomial function f has selected velues of its second derivative f" given in the table above. Which of the following statements must be true?

A) y=-1 only

What are all horizontal asymptotes of the graph of y=5+2^x/1-2^x in the xy-plane

A) 2

What is the slope of the line tangent to the curve y=arctan(4x) at the point at which x=1/4

E) y=-(2x^3/3-14)^1/2

Which of the following is the solution to the differential equation dy/dx=x^2/y with the initial condition y(3)=-2

B) -2

f(x)= cx+d for x<2 =x^2-cx for x>2 Let f be the function defined above, where c and d are constants. If f is differentiable at x=2, what is the value of c+d

A) I only

f(x)= x^2-4/x-2 if x does not =2 =1 if x=2 Let f be the function defined above. Which of the following statements about f are true?

B) -1/2cos(2x)+1/2sin(2x) +C

integration (sin(2x) + c0s(2x)) dx=

D) -x^-1 +C

integration of 1/x^2 dx=

C) 1/2 lnIx^2-4I +C

integration of x/x^2-4 dx

A) -1/2

lim x approaches 0 of 5x^4+8x^2/3x^4-16x^2 is

B) -2

lim x approaches infinity (2x-1)(3-x)/(x-1)(x+3) is