# For what values of x is #f(x)=(x+6)(x-1)(x+3)# concave or convex?

##### 1 Answer

Dec 8, 2017

#### Explanation:

A function is convex where its second derivative is positive and concave where its second derivative is negative. If its second derivative is

Given:

#f(x) = (x+6)(x-1)(x+3)#

#color(white)(f(x)) = x^3+8x^2+9x-18#

We find:

#f'(x) = 3x^2+16x+9#

and:

#f''(x) = 6x+16#

Hence

It has a point of infexion at

graph{(x+6)(x-1)(x+3) [-8.21, 1.79, -25, 22]}