Question

What are the points of inflections for `f(x) = (x^2) - 3/x^3`?

Answer 1

Point of inflection is `xapprox 1.783`

Explanation:

To find points of inflection of a function `f(x)` we need to find second derivative of `f(x)` and equate it to zero. Then find the roots of the polynomial thus obtained.
`f(x)=(x^2)-3/x^3`
or `f(x)=x^2-3x^-3`

First derivative `f'(x)=2x+9x^-4`
Second derivative `f''(x)=2-36x^-5`
For point of inflection `f''(x)=0`
`implies` `2-36x^-5=0`
`implies36x^-5=2`

Solving for `x`
Only root is `x=root(5)(36/2)`