Question: Consider the functions f(x) = x 2 and g(x) = x 3 . (a) Graph f and f on the same set of axes. (b)

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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