The picture below shows the graph y= f'(x) of the derivative of a function y= f(x)....

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 each of the labelled points on the graph, classify the corresponding point on the graph of y= f(x) as on of the following: MAX, MIN, INFL, INT (short for maximum, minimum, inflection point, x-intercept)
A:
B:
C:
D:
E:

 

Expert Answers
thilina-g eNotes educator| Certified Educator

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.