Derivative Behaviors (f, f', f")

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.

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.B.4

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

• x=-5 and -1

• x=-3

• x=0

• no inflection points

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

• an inflection point

• a critical point

• a local maximum

• a local minimum

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

• increasing
• decreasing
• concave up
• concave down

Which of the following describes an interval of f(x) that is both decreasing and concave up?

• f '(x) < 0 and f "(x) < 0

• f '(x) < 0 and f "(x) > 0

• f '(x) > 0 and f "(x) > 0

• f '(x) > 0 and f "(x) < 0

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

• increasing

• decreasing

• concave up

• concave down

f(x) is pictured. Inflection points are most likely at which x values?

• x=0 and 1.5

• x=2 and 2.5

• x=2.25

• x=1

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

• a local maximum.

• a local minimum.

• no maximum or minimum

• a point of inflection

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

• f "(a) is positive

• f "(a) is negative

• f "(a) = 0

• f "(a) is also a local minimum

If f''(x)>0, then what will be true about f'(x) over that same interval?

• f '(x) is constant

• f '(x) is increasing

• f '(x) is decreasing

• f '(x) must have an inflection point in that interval