AP Calculus Unit 2 Review

Taking and Estimating Derivatives

400

The graph of the trigonometric function f is shown above for a≤x≤b. At which of the following points on the graph of f could the instantaneous rate of change of f equal the average rate of change of f on the interval [a,b] ?

At point B.

Rate of Change

200

The graph of the function f, shown above, consists of three line segments. What is the average rate of change of f over the interval 1≤x≤7 ?

0

300

The function f is given by f(x)=1+2sinx. What is the average rate of change of f over the interval [0,π/2]?

4/π

Sin, Cos, Tan, Csc, Sec, Cot

100

The derivative of a function f is given by f′(x)=0.2x+e^0.15x. Which of the following procedures can be used to determine the value of x at which the line tangent to the graph of f has slope 2 ?

A - Evaluate 0.2x + e^0.15x  at x = 2.

B - Evaluate d/dx(0.2x+e^0.15x) at x=2.

C - Solve 0.2x+e^0.15x=2 for x.

D - Solve d/dx(0.2x+e^0.15x)=2 for x.

C - Solve 0.2x+e^0.15x=2 for x.

Derivative Rules

100

If f(x)=x⁶, then f′(x)=

f′(x)= 6x⁵

Differentiation and Continuity

200

Which of the following statements, if true, can be used to conclude that f(3) exists?

1. limx→3 f(x) exists.
2. f is continuous at x=3.
3. f is differentiable at x=3.

Statements 2 and 3 are true.

400

 The graph of the function f, shown above, has a vertical tangent at x=3 and horizontal tangents at x=2 and x=4. Which of the following statements is false?

A - f is not differentiable at x=3 because the graph of f has a vertical tangent at x=3.

B - f is not differentiable at x=−2 and x=0 because f is not continuous at x=−2 and x=0.

C - f is not differentiable at x=−1 and x=1 because the graph of f has sharp corners at x=−1 and x=1.

D - f is not differentiable at x=2 and x=4 because the graph of ff has horizontal tangents at x=2 and x=4.

D - f is not differentiable at x=2 and x=4 because the graph of ff has horizontal tangents at x=2 and x=4.