Verify that the function $f(x)=\frac{x}{x+2}$ satisfies the hypotheses of the Mean Value Theorem on the interval $1,4.$ Then find all numbers $c$ which satisfy the conclusion of the Mean Value Theorem on the given interval.

We can apply the Mean Value Theorem,

$c=-3\sqrt[\phantom{2}]{2}-2$

We can apply the Mean Value Theorem,

$c=+-3\sqrt[\phantom{2}]{2}-2$

We can apply the Mean Value Theorem,

$c=3\sqrt[\phantom{2}]{2}-2$

We can apply the Mean Value Theorem,

$c=\frac{1}{9}$

$f(x)$ does NOT satisfy the hypotheses of the Mean Value Theorem.