# What are the critical values of f(x)=3x^2+2x+5?

##### 1 Answer
Jul 15, 2018

$x = - \frac{1}{3} , y = \frac{14}{3}$

#### Explanation:

Computing the first derivative of $f \left(x\right)$ we get

$f ' \left(x\right) = 6 x + 2$
solving the equation $f ' \left(x\right) = 0$
we get $x = - \frac{1}{3}$

since $f ' ' \left(x\right) = 6 > 0$ we get a minimum (this is global, since we have a parabola)
and we get

$f \left(- \frac{1}{3}\right) = 3 \cdot \frac{1}{9} - \frac{2}{3} + 5 = \frac{1 - 2 + 15}{3} = \frac{14}{3}$