# 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:

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### 1 Answer

**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.