Assume the function f is differentiable over the interval (-co,oo), Classify the

Question

Assume the function f is differentiable over the interval (-co,oo), Classify the following statement as either true or false. If the statement is A function f can have no extrema but still have at least one point of inflection Select the correct choice below O A. The statement is true O B. The statement is false All tunctions have at least one extrema and one port of infection false, explain why C. The statement is false " a function has a point of inflection it must have at least one extrema O D. The statement is false. If a function has no extrema, it cannot have a point of inflection

Explanation / Answer

The statement is true. The point of inflection is where concavity changes. For example f(x)=x+x^3 does not have extrema but has point of inflection.

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