Question

find the absolute maximum and minimum values of the function over the indicated interval, and indicate the x-values at which they occur. f(x) =x^3-3x;[-4,1]

Answer 1

You would begin by finding the first and second derivatives of the given function, because that helps you find maximums and minimums.
Remember, stationary points occur at f'(x) = 0 and often their nature (whether they are a minimum, maximum or point of inflection) can be inspected by inputting the x-values of the stationary points into the function f''(x).
However, as the question is asking for the ABSOLUTE max/mins, that would mean you should also check the endpoints of the domain (so, when x=-4 and when x=1) to see what values of f(x) are produced at those points and whether they are higher/lower than the f(x) values at the stationary points.

Answer 2

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