Question

What are the points of inflection, if any, of `f(x) = x^3-8x^2+13`?

Answer 1

Point of inflection is `x=8/3`

Explanation:

The point of inflection occurs at a point on a curve at which the curve changes from being concave to convex , or vice versa.

This occurs at a point where `f''(x)` i.e. `(d^2f)/(dx^2)=0`.

As `f(x)=x^3-8x^2+13`

`(df)/(dx)=3x^2-16x`

and `(d^2f)/(dx^2)=6x-16`

and point of inflection is given by `6x-16=0` i.e. `x=8/3`

graph{x^3-8x^2+13 [-10, 10, -110.7, 49.3]}