Hello, Jools!

I have a question that gives me the derivative graph of a cubic function.

The graph of is a parabola and is attached below.

Given the graph of , sketch and apossiblegraph of

Identify the following:

a) The intervals where is increasing and decreasing

b) The local maximum and minimum points of

c) The intervals where is concave up and concave down

I have figured out the intervals where g(x) is increasing and decreasing as:

. . . Right!

I have also attached what I have graphed as and . Correct!

With the given points of the parabola: .

. . we can determine its equation: .

Then: .

The extreme values occur where

The second derivative is: .

. .

Therefore: .

Inflection points: .

Therefore: .