
Mean Value Theorem
Suppose that is a function defined and continuous on [2, 2] and that exists on the
open interval (2, 2) . If , and for all in (2, 2) , how
large can possibly be?
I did the follow step, but something goes wrong..
so is infinity ?
and then..
I got confused here...
will ???
and then I tried another way...
Am I wrong again???(Headbang)

Think geometrically! The condition tells you that the function g is convex. The maximum value of g(1) will occur when g''(x) is equal to 4 throughout the interval. If g''(x) is ever greater than 4 (with the endpoints at (2,5) and (2,1) remaining fixed) then the curve will become more convex, forcing g(1) to be smaller.
So let g''(x) = 4. Integrate twice to get . You can find the values of the constants a and b by using the facts that g(2)=5 and g(2)=1, and then you will know what g(1) is.