# In the first Mean Value Theorem #f(b)=f(a)+(b-a)f'(c), a<c<b, f(x) =log_2 x, a=1 and f'(c)=1. How do you find b and c?

##### 1 Answer

Nov 6, 2016

#### Explanation:

#f(b)=f(a)+(b-a)f'(c)#

#f(x)=log_2x#

Note that if

Also note that

If

Now we can also solve for

#f(b)=f(a)+(b-a)f'(c)#

We can replace

#log_2b=0+(b-1)(1)#

#log_2b=b-1#

This can be manipulated to show:

#b=2^(b-1)#

Or:

#2b=2^b#

This occurs at