calculus question

Question

Use the first and second derivatives of the function y = x3-3x2-9x+15 to find the intervals of increase and decrease.

Help!?

Answer 1

First derivative:

 

y' = 3x² - 6x - 9 = 0

 

       3(x² - 2x - 3) = 0

 

       3(x - 3)(x + 1) = 0

 

        x = -1      and       x = 3

 

 

Second derivative:

 

6x - 6 = 0

 

x = 1

 

 

The function is concave down in the interval (-∞, 1) and concave up (1, ∞).  This means that inflection point is located at x=1. 

 

Knowing this, the function is decreasing on the interval (-1, 3).  The function is increasing in the interval (-∞, -1)∪(3, ∞).