Question

let f(x)= sqrt(x-2) for x>=2. what are the possible x values, usually denoted by c in the statement of the mean value theorem, at which f' attains its mean value over the interval 2= 14 years ago

Answer 1

\[f'(c)=\frac{f(5)-f(2)}{5-2}\]
your job to solve this equation for c

\[f'(x)=\frac{1}{2 \sqrt{x-2}} =>f'(c)=\frac{1}{2 \sqrt{c-2}}\]
so we have
\[\frac{1}{2 \sqrt{c-2}}=\frac{\sqrt{5-2}-\sqrt{2-2}}{5-2}\]

Answer 2

\[\frac{1}{2 \sqrt{c-2}}=\frac{\sqrt{3}}{3}\]

\[\frac{3}{2}=\sqrt{3} \sqrt{c-2}\]

square both sides

\[\frac{9}{4}=3(c-2)\]

Answer 3

I believe you can finish this