For a < b real numbers, let ƒ : [a; b] × [a; b] → R be such that (1) for each y € [a, b], the function x → f(x, y) is non-increasing and con- tinuous on [a, b], (2) for each x € [a, b], the function y ↔ f(x, y) is non-decreasing and con- tinuous on [a, b]. Prove that g(x) := f(x, x) is continuous on [a, b].

For a < b real numbers, let ƒ : [a; b] × [a; b] → R be such that (1) for each y € [a, b], the function x → f(x, y) is non-increasing and con- tinuous on [a, b], (2) for each x € [a, b], the function y ↔ f(x, y) is non-decreasing and con- tinuous on [a, b]. Prove that g(x) := f(x, x) is continuous on [a, b].

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter3: Functions

Section3.3: Rates Of Change And Behavior Of Graphs

Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...

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