# Determining the local extrema

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Determine the local extrema of the following function:

(-2/3x^3)-(21/2x^2)-5x+8.

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##### Solution Summary

Critical points are determined and local extrema are found for a function. The solution is detailed and well presented.

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If f is a real valued function with f′(x) positive, f is increasing at x. Let y = f(x) and let s (the slope) = f′(x). Select ε = s/2, and determine h such that f(x+h) - f(x) over h is within ε of s. Within this range, the quotient always exceeds s/2, hence it is positive. The numerator has the same sign as h. When we go forward f ...

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