Question: If f(x) and g(x) are continuous functions that both have an inflection point at x = c, is it true that the sum h(x) =

If f(x) and g(x) are continuous functions that both have an inflection point at x = c, is it true that the sum h(x) = f(x) + g(x) must also have an inflection point at x = c? Either explain why this must always be true or find functions f(x) and g(x) for which it is false.

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