AP Calculus Ch 5 Test

The extreme value theorem states that if a function is ___ on a ___ interval then it will have a(n) ___ and ___ on the interval. (Separate each blank with a comma)

The mean value theorem states that if a function is ___ at every point of the ___ interval and is ___ at every point of its interior, then there is at least one point c in the interval which the ___ rate of change equals the ___ rate of change.

A function is increasing when f'(x)

• >0

• <0

• =0

• DNE

A function is decreasing when f'(x)

• >0

• <0

• =0

• DNE

A function has a local maximum where f'(x)

• changes from positive to negative

• changes from negative to positive

• both

• neither

A function has a local minimum where f'(x)

• changes from positive to negative

• changes from negative to a positive

• both

• neither

A function has an inflection point where f''(x)

• changes from positive to negative

• changes from negative to positive

• both

• neither

When f"(x)>0, the f is

• concave up

• concave down

• increasing

• decreasing

When f"(x)<0, the f is

• concave up

• concave down

• increasing

• decreasing