Question

What are the points of inflection, if any, of `f(x)= 7x^5 - 12x^3 + x`?

Answer 1

Points of inflection are at
`x=0`
`x=+-sqrt(18/35) approx+-.71714`

Explanation:

To find points of inflection, set `f''(x)` equal to zero. To do this, first find f'(x) using the power rule:

`f(x)=7x^5-12x^3+x`

`f'(x)=35x^4-36x^2+1`

`f''(x)=140x^3-72x`

`0=140x^3-72x`
`0=(4x)(35x^2-18)`
`x=0`
`x=+-sqrt(18/35) approx +-.717137`