Consider the functions and on the interval (a) Complete the table and make a conjecture
Chapter 3, Problem 83(choose chapter or problem)
Numerical, Graphical, and Analytic Analysis Consider the functions f(x) = x and g(x) = sin x on the interval \((0, \pi)\).
(a) Complete the table and make a conjecture about which is the greater function on the interval \((0, \pi)\).
(b) Use a graphing utility to graph the functions and use the graphs to make a conjecture about which is the greater function on the interval \((0, \pi)\).
(c) Prove that f(x) > g(x) on the interval \((0, \pi)\). [Hint: Show that \(h^{\prime}(x)>0\) where h = f - g.]
Text Transcription:
(0, pi)
h’(x)>0
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