9. (a) Let f [a, b] → R be continuous and suppose that f(x) > 0 for all x. Show that there is some : L>0 such that f(x)

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9 A Let F A B R Be Continuous And Suppose That F X 0 For All X Show That There Is Some L 0 Such That F X 1 (30.93 KiB) Viewed 46 times

9. (a) Let f [a, b] → R be continuous and suppose that f(x) > 0 for all x. Show that there is some : L>0 such that f(x) > L for all x € [a, b]. (b) Give an example of a continuous function f: R → R satisfying f(x) > 0 for all x, such that no L> 0 satisfies f(x) > L for all x.