The only "hard" part is finding the general derivative.
If , then , , , ...
Do you see the pattern? Obviously, there is an alternating + and -: since this is + for n odd, - for n even.
The denominator of the fraction is a power of 2: .
The numerator is a little harder- it is a product of odd integers from 2n-1 down: 1*3*5*7... We can write that more compactly by filling in the missing evens: . And we can write that denominator as .
The fraction is and the exponent on x+ 1 is .
That is, .
Using that, find a maximum on between 0 and x.