Question

How do you determine all values of c that satisfy the conclusion of the mean value theorem on the interval [11, 23] for `f(x) = sqrt (x-7)`?

Answer 1

Solve `f'(x) = (f(23)-f(11))/(23-11)`. Disregard any solutions outside the interval `(11,23)`

Explanation:

`1/(2sqrt(x-7)) = (sqrt16-sqrt4)/(23-11) = 1/6`

`sqrt(x-7) = 3`

`x=16`

The only value of `c` is `16`.