Graphs of Functions and Their Derivatives

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.

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

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

• f'(x) < 0 (negative)

• f'(x) > 0 (positive)

• f'(x) is increasing

• Can't be determined

When f'(x) changes from positive to negative, there is(are) ...

• a maximum.
• a minimum.
• no extrema.

If f''(x)>0 over the interval (-7,1), then what will be true about f'(x)?

• It's constant
• It's increasing
• It's decreasing
• Cannot be determined

f' is given, which could be f?

• A
• B
• C

If f''(x)<0 over the interval (-7,1), then what will be true about f'(x)?

• It's constant

• It's increasing

• It's decreasing

• Cannot be determined

If f''(x)<0 over the interval (0,3), then what will be true about f(x)?

• f(x) is concave up

• f(x) is increasing

• f(x) is decreasing

• f(x) is concave down