# How do you find the intervals of increasing and decreasing using the first derivative given #y=x(x^2-3)#?

##### 1 Answer

Increasing:

Decreasing:

#### Explanation:

Expand to avoid having to use the product rule.

Use the power rule to differentiate.

Find the critical values. These will occur when the derivative equals

We have three separate intervals we have to check here. There is

Pick test points. If when substituted into the derivative the derivative is negative, the function is *deceasing* over that interval. If the derivative is positive, the function is *increasing* over that interval.

**Test Point 1: #x = -2#**

**Test Point 2: #x = 0#**

**Test Point 3: #x = 2#**

Hopefully this helps!