Consider the function (a) Use a graphing utility to graph the function and estimate the
Chapter 2, Problem 66(choose chapter or problem)
Graphical Analysis Consider the function \(f(x)=\frac{1}{3} x^{3}\).
(a) Use a graphing utility to graph the function and estimate the values of \(f^{\prime}(0), f^{\prime}\left(\frac{1}{2}\right), f^{\prime}(1), f^{\prime}(2)\), and \(f^{\prime}(3)\).
(b) Use your results from part (a) to determine the values of \(f^{\prime}\left(-\frac{1}{2}\right), f^{\prime}(-1), f^{\prime}(-2)\), 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^prime (0), f^prime (1/2), f^prime (1), f^prime (2)
f^prime (3)
f^prime (-1/2), f^prime (-1), f^prime (-2)
f^prime (-3)
f^prime
f^prime (x)
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