AP Calculus BC Semester 1

(16) The function f is given by f(x)=x^4+x^2-2. On which of the following intervals is f increasing?

(0,infinity)

(21) The radius of a circle is decreasing at a constant rate of 0.1 cm per second. In terms of the circumference C, what is the rate of change of the area of the circle, in square centimeters per second?

-(0.1)C

(19) Let f be the function given by f(x)=3e^2x and let g be the function given by g(x)=6x^3. At what value of x do the graph of f and g have parallel tangent lines?

-0.391

If f"(x)=x(x+1)(x-2)^2, then the graph of f has inflection points when x=

-1 and 0 only

If x^2+xy=10, then when x=2, dy/dx=

-7/2

(14) If f(x)=sin(e^-x), then f'(x)=

-e^-xcos(e^-x)

The graph of the function f shown in the figure above has a vertical tangent at the point (2,0) and horizontal tangents at the points (1,-1) and (3,1). For what values of x, -2<x<4, is f not differentiable?

0 and 2 only

Let f and g be differentiable functions with the following properties: (i) g(x)>0 for all x (ii) f(0)=1. If h(x)=f(x)g(x) and h'(x)=f(x)g'(x), then f(x)=

1

(20) If a doesn't = 0, then lim x --> x^2-a^2/x^4-a^4 is

1/2a^2

What is the instantaneous rate of change at x=2 of the function f given by f(x)=(x^2-2)/(x-1)?

2

The graph of a piecewise-linear function f, for -< x<4, is shown above. What is the value of S4-1 f(x)dx?

2.5

(12) The maximum acceleration attained on the interval 0<t<3 by the particle whose velocity is given by v(t)=t^3-3t^2+12t+4 is

21

(13) A particle moves along the x-axis so that its position at the time t is given by x(t)=t^2-6t+5. For what value of t is the velocity of the particle zero?

3

The flow of oil, in barrels per hour, through a pipeline on July 9 is given by the graph above. Of the following, which best approximates the total number of barrels of oil that passed through the pipeline that day?

3000

What is the x-coordinate of the point of inflection on the graph of y=(1/3)x^3+5x^2+24?

5

(17) If f(x)=tan(2x), then f'(pi/6)=

8

(25) If the base b of a triangle is increasing at a rate of 3 inches per minute while its height h is decreasing at a rate of 3 inches per minute, which of the following must be true about the area of the triangle?

A is decreasing only when b>h

(24) Let f be the function given by f(x)=IxI. Which of the following statements about f are true? I. f is continuous at x=0. II. f is differentiable at x=0. III. f has an absolute minimum at x=0.

I and III only

(28) Let f be a function that is differentiable on the open interval (1,10). If f(2)=-5, f(5)=5, and f(9)=-5, which of the following must be true? I. f has at least 2 zeros. II. The graph of f has at least on horizontal tangent. III. For some c, 2<c<5, f(c)=3.

I, II and III only

(27) If g is a differentiable function such that g(x)<0 for all real numbers x and if f'(x)=(x^2-4)g(x), which of the following is true?

f has a relative minimum at x=-2 and a relative maximum at x=2

(18) The graph of a function f is shown above. Which of the following statements about f is false?

f is continuous at x=a

(22) The graphs of the derivatives of the functions f, g, and h are shown above. Which of the functions f, g, or h have a relative maximum on the open interval a<x<b?

f only

If f is continuous for a<x<b and differentiable for a<x<b, which of the following could be false?

f'(c)=0 for some c such that a<c<b

(15) An equation of the line tangent to the graph of y=x+cosx at the point (0,1) is

y=x+1

(26) Which of the following is an equation of the line tangent to the graph of f(x)=x^4+2x^2 at the point where f'(x)=1?

y=x-0.122

If f(x)={lnx for 0<x<2 {x^2ln2 for 2<x<4 , then lim x-->2 f(x) is

Nonexistent

(23) The first derivative of the function f is given by f'(x)=cos^2x/x-1/5. How many critical values does f have on the open interval (0, 10)?

Three