Proof (a) Let and be continuous on the closed interval If and prove that there exists
Chapter 2, Problem 128(choose chapter or problem)
Proof
(a) Let \(f_{1}(x) \text { and } f_{2}(x)\) be continuous on the closed interval [a, b]. If \(f_{1}(a)<f_{2}(a) \text { and } f_{1}(b)>f_{2}(b)\), prove that there exists c between a and b that \(f_{1}(c)=f_{2}(c)\).
(b) Show that there exists c in \([0, \pi / 2]\) such that cos x = x. Use a graphing utility to approximate c to three decimal places.
Text Transcription:
f_1 (x) and f_2 (x)
f_1 (a) < f_1 (b) > f_2 (b)
f_1 (c) = f_2 (c)
[0, pi/2]
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