# How do you find the critical points for f(x)= (2x^2+5x+5)/(x+1)?

Apr 24, 2018

$\left(- 2 , - 3\right) , \left(0 , 5\right)$

#### Explanation:

The derivative is either 0 or undefined:

$f ' \left(x\right) = \frac{\left(4 x + 5\right) \left(x + 1\right) - 1 \left(2 {x}^{2} + 5 x + 5\right)}{x + 1} ^ 2$
$f ' \left(x\right) = \frac{2 {x}^{2} + 4 x}{x + 1} ^ 2$

$f ' \left(x\right) = 0$
$\frac{2 {x}^{2} + 4 x}{x + 1} ^ 2 = 0$
$2 x \left(x + 2\right) = 0$
$x = - 2 , x = 0$

$f \left(- 2\right) = - 3$
$f \left(0\right) = 5$