Find where the function is increasing and decreasing

Question

The derivative of a polynomial is f'(x) = (x-3)^2 (x+7)

Answer 1

Set the derivative equal to zero.

 

(x - 3)(x - 3)(x + 7) = 0

 

 

Your critical points are located at   x= -7    and   x = 3.

 

Now you must evaluate the derivative around these critical points.  If the derivative is positive, then the function is increasing.   Otherwise, function is decreasing.

 

Evaluate these derivatives:

 

f'(-8) ,    f'(0)  ,  and     f'(4)