# Math Help - Derivatives question

1. ## Derivatives question

Given that $y=\frac{x^3}{3}-x^2+x$, find $\frac{dy}{dx}$. Hence show that $\frac{dy}{dx}\geq 0$ for all x.

Please show complete working out. Any help will be appreciated.

2. Originally Posted by Mr Rayon
Given that $y=\frac{x^3}{3}-x^2+x$, find $\frac{dy}{dx}$. Hence show that $\frac{dy}{dx}\geq 0$ for all x.

Please show complete working out. Any help will be appreciated.
$y=\frac{x^3}{3}-x^2+x$

$y' = x^2 - 2x + 1$

This can be factorised:
$x^2 - 2x + 1 = (x-1)^2$

Since y' is a square number, it has to be zero or positive for all x.