Given the function $f (x) = = \frac{x^{2}}{4 x + 8}$ $f(x)==x^2/(4x+8)$ , how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [-3,-1] and find the c?

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Answer 1 · 2016-10-21T16:35:57

The mean value theorem is not applicable since $f (x)$ $f(x)$ is not continuous on the interval

$f (x) = \frac{x^{2}}{4 x + 8}$ $f(x)=x^2/(4x+8)$

The domain of $f (x)$ $f(x)$ is $RR-(-2)$ since we cannot divide by 0:
$4x+8!=0$
$x!=-2$
So $f(x)$ is not continuous on the interval (-3,-1)

So we cannot apply the Mean Value Theorem

Given the function f(x)==x^2/(4x+8)f(x)==x24x+8f(x)==x^2/(4x+8), how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [-3,-1] and find the c?