Solution: Graphical Reasoning Consider the function (a) Use a graphing utility to graph
Chapter 3, Problem 60(choose chapter or problem)
Graphical Reasoning Consider the function \(f(x)=\frac{1}{3} x^{3}\).
(a) Use a graphing utility to graph the function and estimate the values of \(f^{\prime}(0), f^{\prime}\left(\frac{1}{2}\right), f^{\prime}(1), f^{\prime}(2), \text { and } f^{\prime}(3)\)
(b) Use your results from part (a) to determine the values of \(f^{\prime}\left(-\frac{1}{2}\right), f^{\prime}(-1), f^{\prime}(-2), \text { and } f^{\prime}(-3)\)
(c) Sketch a possible graph of \(f^{\prime}\).
(d) Use the definition of derivative to find \(f^{\prime}(x)\).
Text Transcription:
f(x)=1/3 x^3
f^(0), f^(1/2), f^(1), f^(2), and f^(3)
f^(-1/2), f^(-1), f^(-2), and f^(-3)
f^
f^(x)
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