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An Exceptional Exponential Function

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We show that there is a link between a standard calculus problem of finding the best view of a painting and special tangent lines to the graphs of exponential functions. Surprisingly, the exponential function with the "best view" is not the one with the base e. A similar link is established for families of functions obtained by composing exponential functions with a fixed linear function. The key tool in the proof is the Lambert W function.

Document Type: Research Article

Publication date: 2006-11-01

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