The graph of the derivative f \' of a function f is shown. (a) On what intervals

Question

The graph of the derivative f ' of a function f is shown.

(a) On what intervals is f increasing? (Enter the interval that contains smaller numbers first.)

(______, _____) U (______, _____)

(b) On what intervals is f decreasing? (Enter the interval that contains smaller numbers first.)

(______, _____) U (______, _____)

(c) At what values of x does f have a local maximum or minimum?

x= ______ (smallest value)

x= ______

x= ______ (largest value)

The graph of the derivative f ' of a function f is shown. On what intervals is f increasing? (Enter the interval that contains smaller numbers first.) On what intervals is f decreasing? (Enter the interval that contains smaller numbers first.) At what values of x does f have a local maximum or minimum?

Explanation / Answer

(a) F(x) is increasing when f'(x) > 0

Hence in this case, it is

(0,1)U(3,5)

(b) f(x) is decreasing when f'(x) < 0

Hence the answer is

(1,3)U(5,6)

(c) f(x) has a maxima or minima when f'(x) = 0

hence the answer is

x = 3 (smallest value), because f'(x) turned from negative to positive

x = 1, 3 (larger values), because f'(x) turned from positive to negative

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