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.
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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.
Hi, can you clarify this @lucas.coutinho? Wouldn’t the function also be decreasing (see graph below)? I plotted it and can see the part where the derivative is 0 (flat part) is the maximum, which is 0.7. But if this wasn’t graphed, how would I know if it is a max or minimum from looking at the function?
If you take the 2nd partial derivative, you can determine if the function is convex.