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.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 36E
Related questions
Question
![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F85464341-e972-46e7-84fb-f0ef36f44755%2F283af056-a0df-4019-891c-9d16a9e76b2a%2Fcft774f_processed.jpeg&w=3840&q=75)
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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