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]}