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PROBLEM: Functions tangent to their product

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Try these on your TI-81 or TI-82 or TI-83 or TI-85, etc.

• A. Find linear functions f(x) and g(x) such that the function h(x) = f(x).g(x) is tangent to each of the linear functions.

• B. Find quadratic functions f(x) and g(x) such that the function h(x) = f(x).g(x) is tangent to each of the quadratic functions in two places.