# What are the critical values, if any, of # f(x)= x^2sinx +sinxcos^2x in [0,pi]#?

##### 1 Answer

#### Explanation:

Given:

**One way to find the critical values is to graph and find the maximum using a graphing calculator** :

relative max:

graph{x^2sin x + sinx( cos x)^2 [-2, 3.14159, -2, 5]}

**The second way is to find the first derivative and set it equal to zero** and solve for

Find the first derivative using the product rule:

For the first part of the function let

Let

**Find critical values** :

This is a difficult problem. The easiest way to solve is to use a graphing calculator to graph the derivative and then solve for the zero (

graph{x^2 cos x + 2x sin x -2(cos x)^2 sin x + (cos x)^3 [-2, 3.14159, -2, 5]}