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Conjecture Consider g(x) = x³. the functions f(x) = x2 and (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) = ", where n is an integer and n 2 2. (d) Find f'(x) if f(x) = x*. Compare the result with the conjecture in part (c). Is this a proof of your conjecture? Explain.

Conjecture Consider g(x) = x³. the functions f(x) = x2 and (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) = ", where n is an integer and n 2 2. (d) Find f'(x) if f(x) = x*. Compare the result with the conjecture in part (c). Is this a proof of your conjecture? Explain.

College Algebra
College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Functions And Their Graphs
Section2.6: Combinations Of Functions: Composite Functions
Problem 69E
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Conjecture Consider g(x) = x³. the functions f(x) = x2 and (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) = ", where n is an integer and n 2 2. (d) Find f'(x) if f(x) = x*. Compare the result with the conjecture in part (c). Is this a proof of your conjecture? Explain.
Transcribed Image Text:Conjecture Consider g(x) = x³. the functions f(x) = x2 and (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) = ", where n is an integer and n 2 2. (d) Find f'(x) if f(x) = x*. Compare the result with the conjecture in part (c). Is this a proof of your conjecture? Explain.
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