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www.dummies.com/education/math/calculus/how-to-find-local...

All local maximums and minimums on a function’s graph — called local extrema — occur at critical points of the function (where the derivative is zero or undefined). (Don’t forget, though, that not all critical points are necessarily local extrema.) The first step in finding a function’s local extrema is to find its critical numbers […]

tutorial.math.lamar.edu/classes/calcI/absextrema.aspx

This is a good thing of course. We don’t want to be trying to find something that may not exist. Next, we saw in the previous section that absolute extrema can occur at endpoints or at relative extrema. Also, from the previous section that we know that the list of critical points is also a list of all possible relative extrema.

www.coolmath.com/.../12-relative-extrema-minimums-maximums-01

Another huge thing in Calculus is finding relative extrema. Check out this graph: The tops of the mountains are relative maximums because they are the highest points in their little neighborhoods (relative to the points right around them): Suppose you're in a roomful of people (like your classroom.) Find the tallest person there. (It's usually ...

Math · AP®︎ Calculus AB · Applying derivatives to analyze functions · Using the first derivative test to find relative (local) extrema Finding relative extrema (first derivative test) The first derivative test is the process of analyzing functions using their first derivatives in order to find their extremum point.

www.dummies.com/education/math/calculus/how-to-find-local...

How to Find Local Extrema with the Second Derivative Test. The Second Derivative Test is based on two prize-winning ideas: First, that at the crest of a hill, a road has a hump shape — in other words, it’s curving down or concave down. And second, at the bottom of a valley, a road is cup-shaped, so it’s curving up or concave up. ...

pblpathways.com/calc/C12_1_3.pdf

extrema at the corresponding critical point. Example 6 Find the Relative Extrema of a Function Find the location of the relative extrema of the function fx xxx() 4 21 18 5 32 Solution The first derivative test requires us to construct a number line for the derivative so that we can identify where the graph is increasing and decreasing.