Question

What are the points of inflection, if any, of #f(x)=2x^3 + 8x^2 #?

Answer 1

At `x=-4/3` there is point of inflection

Explanation:

Given -

`y=2x^3+8x^2`

To find the point of inflection put send derivative equal to zero and find the value of `x`

`dy/dx=6x^2+16x`

`(d^2y)/(dx^2)=12x+16`

`(d^2y)/(dx^2)=0 => 12x+16=0`

`x=(-16)/12=-4/3`

graph{2x^3+8x^2 [-10, 10, -5, 5]}