How to find absolute maximum of a function calculus

Start of by calculating the first derivative. Thanks to that we'll know the slope of the function in every point of it.

After you've done that you can set the derivative to be equal to 0 and find the x1 for which is verified this condition (note: there could be multiple solutions).

You'll obtain a (or more) couple(s) of coordinates: (x1, f(x1)).

Then examine the function's behavior near that point. See what happens at its right and at its left (for x>x1 and x<x1). If the derivative will be negative in both cases, that will be a maximum, if in both cases it will be positive, it will be a minimum and if one will be negative and the other positive, it will just be a point where the slope = 0, not a maximum and not  a minimum.

Note: I forgot to say that if a derivative set to 0 has no solutions, it means that the function has no minimum or maximum.

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step-by-step explanation: