Question

How do you determine all values of c that satisfy the mean value theorem on the interval [3,6] for `f(x)=(x-4)^2-1`?

Answer 1

`c=9/2`

Explanation:

`f'(x) =2(x-4)`

Mean Value Theorem
`f'(c)=(f(b)-f(a))/(b-a)`

`2(c-4)=(f(6)-f(3))/(6-3)`

`2c-8=(3-0)/3`

`2c-8 =1`

`2c=9`

`c=9/2`