Coin Toss - How to know a derivative of a function is maximize or minimize

In the Optimization of log-loss - Part 1, how do we know the derivative of the function:
p^7(1-p)^3 = 0 is a maximize. In course 1, we know if a derivative is equal to zero it can be minimized or maximized.

Hi @impossibleno1,

In this case, it is the way the problem is defined that tells us that we need to maximize the function. Since we know that p \in [0,1] and the function is always increasing between 0 and 1, and in the boundaries, the function is 0 and the fact that the function has only 1 point of derivative 0 that lies in [0,1], this is enough to tell this is a maximum.

If you want to be very precise, though, you can compute the second derivative of the function and show that it is negative in the point where it is 0.