What are the critical values, if any, of $f (x) = \frac{3 x^{2} + 2 x + 5}{4 x^{2} + 2 x + 1}$ $f(x)=(3x^2+2x+5)/(4x^2+2x+1)$ ?

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Answer 1 · 2017-04-07T08:50:56

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

Here, you do so by applying the quotient rule.

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

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

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

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)

What are the critical values, if any, of f(x)=3x2+2x+54x2+2x+1f(x)=(3x^2+2x+5)/(4x^2+2x+1)?