You're on the right track, but you need to set the derivative equal to zero to find a maximum. Even though it can't be easily factored, you can still use the quadratic formula to find your values of t. You'll use the second derivative to see if it's a maximum, minimum, or inflection point...
Homework Statement
For a positive integer k, the number M_k = 2^k - 1 is called the kth Mersenne number. Let p be an odd prime, and let q be a prime that divides M_p.
a. Explain why you know that q divides 2^{q-1}-1.
I have done this already using Euler's theorem, since q prime implies...