Given that \( f \) and \( g \) are continuous on \([a, b]\), that \( f(a) < g(a) \), and \( g(b) < f(b) \), show that there exists at least one number \( c \) in \((a, b)\) such that \( f(c) = g(c) \). HINT: Consider \( f(x) - g(x) \).

Explanation of the answer is as follows

Answered: Given that f and g are continuous on…

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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Given that f and g are continuous on [a, b], that f(a) < g(a), and g(b) < f(b), show that there exists at least one number c in (a, b) such that f(c) = g(c). HINT: Consider f(x) – g(x).