f(x) = 2x/(6x+12)
f(1) = 1/9
f(4) = 2/9
(f(4)-f(1))/(4-1) = 1/27
The MVT says that there is c in [1,4] such that f'(c) = 1/135
f'(x) = 2/3 (x+2)^-2
So,
2/3 (c+2)^-2 = 1/27
c = 2.24
which is inside [1,4]
18) Find all numbers c that satisfy the conclusion of the Mean Value Theorem for the following function and interval. Enter the values in increasing order and enter N in any blanks you don't need to use.
f(x)=2x/6x+12,[1,4]
1 answer