# How do you find the exact relative maximum and minimum of the polynomial function of #g(x) =x^3 + 6x^2 – 36#?

##### 1 Answer

See below.

#### Explanation:

Given

To find the maximum and minimum of the function find first derivative and set it equal to zero.

After factoring out

Since

For

Hence

Now to ascertain the second derivative of the given function

At the first point

Similarly at the point

Verify by drawing a graph with the graphing tool

graph{y=x^3+6x^2-36 [-80, 80, -40, 40]}