Question

What are the points of inflection, if any, of `f(x)= x^5 -2 x^3 + 3 x^2-2`?

Answer 1

I am using the graph to approximate the location of the point of

inflexion for x little less than `-0.5`,

Explanation:

`f''(x)=20x^3-12x^2+6; f''(0)=-2<0 and f''(-1)=2 >0`.

So, f'' = 0 for x close to `-0.5`. The value correct to a specified

number of significant digits can be obtained, using a numerical

iterative method, with starer as `-0.5`. If required, I would give this

in the next edition.
graph{x^5-2x^3+3x^2-2 [-10, 10, -5, 5]}