Calculus AB Section I, Part A

Let f be the function with derivative given by f'(x)=x^2-(2/x). On which of the following intervals is f decreasing?

(0, cubed root(2)]

The integral of (x^2)(cos(x^3))dx=

(1/3)sin(x^3) + C

The rate of change of the volume, V, of water in a tank with respect to time, t, is directly proportional to the square root of the volume. Which of the following is a differential equation that describes this relationship?

(dV/dt)=k*sqrt(V)

If f(x)=ln(x+4+e^(-3x)), then f '(0) =

-2/5

The derivative g' of a function g is continuous and has exactly two zeros. Selected values of g' are given in the table above. If the domain of g is the set of all real numbers, then g is decreasing on which of the following intervals?

-2<=x<+2 only

If y=(2x+3)/(3x+2), then dy/dx=

-5/(3x+2)^2

On [0, pi/4], the integral of sinx dx=

-sqrt(2)/2 + 1

The second derivative of the function f is given by f''(x)=x(x-a)(x-b)^2. The graph of f'' is shown above. For what values of x does the graph of f have a point of inflection?

0 and a only

The graph of f', the derivative of the function f, is shown above. Which of the following statements is true about f?

f is increasing for -2<=x<=0.

The function f has the property that f(x), f '(x), and f "(x) are negative for all real values x. Which of the following could be the graph of f ?

f(x) must be decreasing and concave down

For x>=0, the horizontal line y= 2 is an asymptote for the graph of the function f . Which of the following statements must be true?

limit, as x approaches infinity, of f(x)=2

A particle moves along the x-axis so that at time t>=0 its position is given by x(t)=2t^3-21t^2+72t-53. At what time t is the particle at rest?

t=3 and t=4

Let f be the function given by f(x)=2xe^x. The graph of f is concave down when

x< -1

Let f be the function defined by f(x)=4x^3-5x+3. Which of the following is an equation of the line tangent to the graph of f at the point where x = - 1?

y=7x+11

A curve has slope 2x + 3at each point (x,y) on the curve. Which of the following is an equation for this curve if it passes through the point (1,2)?

y=x^2+3x-2

If the line tangent to the graph of the function f at point (1,7) passes through the point (- 2,-2), then f'(1) is

3

If y=(x^2)sin(2x), then dy/dt=

2x(sin2x + xcos2x)

d/dx [on [0,x^2] the integral of sin(t^3)dt]=

2xsin(x^6)

Using the substitution u=2x+1, on [0,2] the integral of sqrt(2x+1)dx is equivalent to

1/2 of, on [1,5], the integral sqrt(u)du

As x approaches infinity, the limit of (x^3-2x^2+3x-4)/(4x^3-3x^2+2x-1)=

1/4

Let f be the function defined by f(x)=x^3+x. if g(x)=f^(-1)(x) and g(2)=1, what is the value of g'(2)?

1/4

Let g be a twice-differentiable function with g'(x)>0 and g''(x)>0 for all real numbers x, such that g(4)=12 and g(5)=18. Of the following, which is a possible value for g(6)?

27

What is the slope of the tangent to the curve 3y^2 -2x^2=6-2xy at the point (3,2)?

4/9

If y=(x^3=1)62, then dy/dx=

6x^2(x^3=1)

The graph of f ', the derivative of f , is the line shown in the figure above. If f (0) = 5, then f (1) =

8

Let f be the function given above. Which of the following statements are true about f ?

I and II only

The graph of a function f is shown above. At which value of x is f continuous, but not differentiable?

a