# How do you find the intervals of increasing and decreasing using the first derivative given #y=x^3-4x#?

##### 2 Answers

Increasing:

Decreasing:

#### Explanation:

We start by finding the derivative (use the power rule).

#y' = 3x^2 - 4#

Critical numbers will occur when the derivative is

#0 = 3x^2 - 4 -> x^2 = 4/3 -> x = +-2/sqrt(3)#

We now select a test point in one of the intervals, let it be

#y'(0) = 3(0)^2 - 4 = -4#

Since this value is negative, the function is decreasing here. This means it must be increasing on

Finally, notice how I write the intervals as open intervals (aka the round parentheses instead of the closed parentheses). This is because at the critical values the function is neither increasing nor decreasing.

Hopefully this helps!

The intervals of increasing are

#### Explanation:

We calculate the first derivative

Critical points are when

We build a variation chart

graph{x^3-4x [-10, 10, -5, 5]}