MATH 1007 Lecture Notes - Lecture 9: Maxima And Minima, Minimax, Farad
6 Apr 2016
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Absolute extrema of a coninuous funcion on a closed interval: Ex: ind the absolute maxiumum and minimum of f(x)=lnx/x on the interval [1,3] First ind the domain it is (0, ) F(e)= lne/e = 1/e = about 0. 368 * global max. *if f"(x) > 0 on an interval, then f is increasing on that interval. *if f"(x) < 0 on an interval, then f is decreasing on that interval. Suppose that c is a criical number of coninuous funcion f *if f" changes sign from (+) to (-) at c, then f has a local maximum. *if f" changes sign from (-) to (+) at c, then f has a local minimum. *if f" does not change sign at c, then f has no local max/min at c at c at c. Remember how to ind the decreasing/increasing thing in the table from gr.
