# How do you determine critical points for any polynomial?

Mar 29, 2018

by finding the first derivative of the polynomial and find the values of the variable at which the first derivative equals zero

#### Explanation:

for example:
$y = {x}^{2} - 2 x$
by finding the first derivative
$y ' = 2 x - 2$
so $y ' = 0$ when $2 x - 2 = 0$
and by solving it the $x$ co_ordinate of the critical point of the function $= 1$
so the critical point will be $\left(1 , - 1\right)$