The picture below shows the graph y= f'(x) of the derivative of a function y= f(x).  http://webwork.marianopolis.com:81/wwtmp/Haldane_course/gif/1131348-1958-setNYA-Assignment-9prob9image1.png For...

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thilina-g | College Teacher | (Level 1) Educator

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A - This is the graph of the derivative of the function f(x). Around A f'(x) is changing from negative to positive. That means at A, we have a minimum.

B - At B the derivative is maximum and on the otherhand the second derivative is zero. We have a rising inflection point at B

C - The sign of first derivative changes from positive to negative. Therefore at C we have a maximum.

D - Again we have a similar situation like B. So we have an inflection point at D also. But this is a falling inflection point.

E - At E also we have derivative changing from negative to positive. So we have a minimum at E also.

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