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