# How do you determine all values of c that satisfy the mean value theorem on the interval [6,10] for #f(x)= ln (x-5)#?

##### 1 Answer

#### Explanation:

The function

We can therefore most certainly use the mean value theorem to solve for

We start by finding the derivative of

Then

#dy/dx = 1/u xx 1#

#dy/dx= 1/(x - 5)#

By the mean value theorem:

#1/(c- 5) = (f(10) - f(6))/(10 - 6)#

#1/(c- 5) =(ln5 - ln1)/4#

#1/(c- 5) = (ln5 - 0)/4#

#4 = (c- 5)ln5#

#4 = cln5 - 5ln5#

#4 + ln3125 = cln5#

#c= (4 + ln3125)/ln5 ~= 7.485#

Hopefully this helps!