Using a Function Consider the function (a) Use a graphing utility to graph and (b) Is a
Chapter 4, Problem 69(choose chapter or problem)
Using a Function Consider the function
\(f(x)=3 \cos ^{2}\left(\frac{\pi x}{2}\right)\).
(a) Use a graphing utility to graph f and f'.
(b) Is f a continuous function? Is f' a continuous function?
(c) Does Rolle's Theorem apply on the interval [-1, 1]? Does it apply on the interval |1, 2]? Explain.
(d) Evaluate, if possible, \(\lim _{x \rightarrow 3^{-}} f^{\prime}(x)\) and \(\lim _{x \rightarrow 3^{+}} f^{\prime}(x)\).
Text Transcription:
f(x)=3 cos^2 (pi x/2)
lim_x rightarrow 3^- f’(x)
lim_x rightarrow 3^+ f’(x)
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