Consider the functions f(x) = x 2 and g(x) = x 3 . (a) Graph f and
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Consider the functions f(x) = x2 and g(x) = x3.
(a) Graph f and f′ on the same set of axes.
(b) Graph g and g′ on the same set of axes.
(c) Identify a pattern between f and g and their respective derivatives. Use the pattern to make a conjecture about h′(x) if h(x) = xn, where n is an integer and n ≥ 2.
(d) Find f′(x) if f(x) = x4. Compare the result with the conjecture in part (c). Is this a proof of your conjecture? Explain.
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Related Book For
Calculus Of A Single Variable
ISBN: 9781337275361
11th Edition
Authors: Ron Larson, Bruce H. Edwards
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