Unit 5 Review

• local maximum

• local minimum

• stationary point

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

• x=-5 and -1
• x=-3
• x=4
• no inflection points

For a function f(x), f'(-3) = 5 indicates f(x) is ___________ at x=-3.

• increasing
• decreasing
• concave up
• concave down

What are all intervals on which the graph of f is concave down?

• -1 < x < 1

• 0 < x < 2

• 1 < x < 3 ONLY

• -2 < x < -1 ONLY

• -2 < x < -1 AND 1 < x < 3

The concavity of a function is described by its _______________.

• first derivative
• second derivative
• third derivative
• expression

For a function g(x), g''(3)=-8 indicates that g(x) is ____________ at x=3.

• increasing
• decreasing
• concave up
• concave down

The graph of f''(x) is pictured. Over which interval is f(x) concave up?

• (-infinity, 3)
• (-5, -1)
• nowhere
• (0, 4)

f' is given, which could be f?

• A
• B
• C

 If (a,b) is a local minimum, then what will be true about f''(a)?

• It's postive
• It's negative
• It's zero
• Cannot be determined