The function f(x) = ex has the properties f (x) = f(x) and f(0) = 1. Explain why f(x) is
Chapter 3, Problem 60(choose chapter or problem)
The function f(x) = ex has the properties f (x) = f(x) and f(0) = 1. Explain why f(x) is the only function with both these properties. [Hint: Assume g (x) = g(x), and g(0) = 1, for some function g(x). Define h(x) = g(x)/ex, and compute h (x). Then use the fact that a function with a derivative of 0 must be a constant function.]
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