Critical number :

A critical number of a function $\"\"$ is a number $\"\"$ in the domain of $\"\"$ such that either $\"\"$ or $\"\"$ does not exist.

$\"\"$

The function is $\"\"$ .

$\"\"$ is differentiable at all values of $\"\"$ because it is a polynomial.

Therefore, solutions of $\"\"$ are the critical numbers.

Differentiate $\"\"$ on each side with respect to $\"\"$ .

$\"\"$

$\"\"$ .

Equate $\"\"$ to zero.

$\"\"$

$\"\"$ and $\"\"$

Find the solutions of the quadratic equation $\"\"$ :

$\"\"$

The solutions of $\"\"$ are imaginary numbers, they are not considered.

The critical number is $\"\"$ .