MyAP Classroom Quizzes for Dervivative Test

Selected values of a function g are shown in the table above. What is the average rate of change of g over the interval [−3,3] ?

B. (−4)−12/3−(−3)

d/dx(1/x^3 − 1/x + x^2) at x=−1 is

B. -4

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?

B. 0 and 2 only

Selected values of a function g are shown in the table above. What is the average rate of change of g over the interval [−2,2] ?

B. 5−(−3)/2−(−2)

In the xy-plane, the line x + y = k , where k is a constant, is tangent to the graph of y = x2 + 3x + 1 . What is the value of k ?

A. -3

Shown above is the graph of the differentiable function f, along with the line tangent to the graph of f at x=2. What is the value of f′(2) ?

A. 1/2

Let f be a differentiable function with f(1)=3. The graph of f′, the derivative of f, is shown above. Which of the following statements is true about the line tangent to the graph of f at x=1 ?

A. The tangent line has slope 2 and passes through the point (1,3).

Let f be a differentiable function with f(1)=−2. The graph of f′, the derivative of f, is shown above. Which of the following statements is true about the line tangent to the graph of f at x=1 ?

A. The tangent line has slope −1 and passes through the point (1,−2).

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

A. a

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

C

Let f be the function defined by f(x)=e2x. The average rate of change of f over the interval [1,b] is 20, where b>1. Which of the following is an equation that could be used to find the value of b ?

C.

Let f be the function defined by f(x)=secx+cscx. Which of the following expressions is the average rate of change of f over the interval [π4,3π8] ?

C.

Let f be the function given by f(x)=x3−6x2+8x−2. What is the instantaneous rate of change of f at x=3?

C. -1

If f(x)=x, then f′(5)=

C. 1

What is the average rate of change of the function f given by f (x) = x^4 - 5x on the closed interval [0, 3]?

C. 22

If f(x)=x^(3/2), then f'(4) =

C. 3

An equation for the line tangent to the graph of the differentiable function f at x=2 is y=9x−12. Which of the following statements must be true? f(0)=−12 f(2)=6 f′(2)=9

C. II and III only

An equation for the line tangent to the graph of the differentiable function f at x=3 is y=4x+6. Which of the following statements must be true? f(0)=6 f(3)=18 f′(3)=4

C. II and III only

Let f be the function defined by f(x)=2x3−x. Which of the following expressions is the average rate of change of f on the interval [1,3] ?

C. f(3)−f(1)/3−1

Let f be the function defined by f(x)=2sinx+cosx. The average rate of change of f over the interval [0,b] is 0.05, where b>0. Which of the following is an equation that could be used to find the value of b ?

C. f(b)−f(0)/b−0=0.05

Let f be a differentiable function. The figure above shows the graph of the line tangent to the graph of f at x=0. Of the following, which must be true?

C. f′(0)=f(0)

f(x)={x+2if x≤3 {4x−7if x>3 Let f be the function given above. Which of the following statements are true about f ? I. limx→3f(x) exists. II. f is continuous at x = 3. III. f is differentiable at x = 3

D. I and II 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)= :

E. 1

If f(x) = 2 + | x-3 | for all x, then the value of the derivative f'(x) at x = 3 is

E. nonexistent

f(x)={2x+5 for x<−1 {−x^2+6for x≥−1 If f is the function defined above, then f′(−1) is

E. nonexistent

f(x)={3x+5 when x<−1 {−x^2+3when x≥−1 If f is the function defined above, then f′(−1) is

E. nonexistent

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

D. 2

If f(x)=e^2x(x3+1), then f′(2)=

D. 30e^4