# How do you determine where the function is increasing or decreasing, and determine where relative maxima and minima occur for #y = x^3 - 3x^2 - 9x +15#?

##### 1 Answer

At

#### Explanation:

A function is increasing, when the value of its derivative at that point is positive and is decreasing, when the value of its derivative at that point is negative.

At maxima and minima, the value of derivative is

Further, at maxima, second derivative is negative and at minima, second derivative is positive.

Derivative of

Factorizing

However, as elsewhere the functions takes lower value than the minima or higher value than the maxima these are relative minima and maxima.

graph{x^3-3x^2-9x+15 [-10, 10, -25, 25]}