# What are the critical values, if any, of f(x)=(3x^2+2x+5)/(4x^2+2x+1)?

Apr 7, 2017

In order to find the critical points, you need to find the derivative, f' of the function.

#### Explanation:

Here, you do so by applying the quotient rule.

$u = 3 {x}^{2} + 2 x + 5$
$u ' = 6 x + 2$
$v = 4 {x}^{2} + 2 x + 1$
$v ' = 8 x + 2$

When you apply the quotient rule, you should obtain the equation of

$- 2 {x}^{2} - 34 x - 8$

Solve for zeros

Then, plug in the values that make x zero into the original equation and you should obtain a max point of (-0.239,6.254)