Conjecture Consider the functions and (a) Graph and on the same set of coordinate axes
Chapter 3, Problem 92(choose chapter or problem)
Conjecture Consider the functions \(f(x)=x^{2}) and \(g(x)=x^{3}\)
(a) Graph \(f\) and \(f^{\prime}\) on the same set of coordinate axes.
(b) Graph \(g\) and \(g^{\prime}\) on the same set of coordinate axes.
(c) Identify a pattern between \(f\) and \(g\) and their respective derivatives. Use the pattern to make a conjecture about \(h^{\prime}(x) \text { if } h(x)=x^{n}\), where is an integer and \(n \geq 2\)
(d) Find \(f^{\prime}(x)\text{ if }f(x)=x^4\). Compare the result with the conjecture in part (c). Is this a proof of your conjecture? Explain
Text Transcription:
f(x)=x^2
g(x)=x^3
f
f^
g
g^
h^(x) if h(x)=x^n
n geq 2
f^(x) if f(x)=x^4
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