Derivative of an Exponential Function Problem: Figure 15-5j shows the graph of the
Chapter 15, Problem 25(choose chapter or problem)
Derivative of an Exponential Function Problem: Figure 15-5j shows the graph of the exponential function f(x) = 2x . Figure 15-5j a. If the multiply by the original exponent, and decrease the exponent by 1 pattern worked for exponential functions, what would f (x) equal for this function? b. Find f (0) using the results of part a. Based on the graph in Figure 15-5j, explain why this number could not possibly be the derivative of f(x) = 2x at x = 0. c. Explain why the counterexample in part b constitutes a proof that the derivative of an exponential function cannot be found using the same shortcut as for the derivative of a power function.
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