Graphs of Functions and Their Derivatives

7.

• (A)

• (B)

• (C)

• (D)

Which graph is the derivative of the top graph?

• A

• B

• C

• D

f' is given, which could be f?

• A

• B

• C

Which one of the following statements is always true?

• When a graph is increasing, its derivative is negative.

• When a graph is decreasing, so is its derivative.

• When a graph is decreasing, its derivative is negative.

• When a graph is increasing, so is its derivative.

Select the correct derivative of f(x).

• A.

• B.

• C.

• D.

• A

• B

• C

• D

If given f'(x) how would you find the intervals which the graph f(x) has a positive slope?

• f'(x) < 0 (negative)

• f'(x) > 0 (positive)

• f'(x) is increasing

• Can't be determined

f(x) is a polynomial function. Which one of the following statements is FALSE?

• f(x) has a derivative of zero when the graph of f has a relative min or max.

• If the derivative of f(x) changes from positive to negative at some point, then the graph of f has a relative minimum at that point.

• If the derivative of f(x) is always positive, then the graph of f has no relative extrema.

• If the graph of f is always increasing, then the derivative of f(x) is never negative.

f''(x) is pictured. Which x values are inflection points of f(x)?

• x=-5 and -1

• x=-3

• x=4

• no inflection points

For a function g(x), g'(-2)=0 indicates that x=-2 is ________________.

• an inflection point

• a critical point

• a relative maximum

• a relative minimum