Question

How do you find the critical points for `f(x)=8x^3+2x^2-5x+3`?

Answer 1

Hello,

Calculate the derivative

`f'(x) = 24x^2 + 4x - 5`.

Solve `f'(x) = 0`. To do that, Calculate the discriminant `Delta = 4^2 - 4\times 24 times (-5) = 496`.

The critical points of `f` are the zeros of `f'`. So they are
`(-4-sqrt(496))/48` and `(-4+sqrt(496))/48`.

You can simplify, because `496 = 16 \times 31` :
`(-1-sqrt(31))/12` and `(-1+sqrt(31))/12`.