Explanation Information used: A function f ( x ) is always concave up , if f ″ ( x ) > 0 for every real number x and a function f ( x ) is always concave down, if f ″ ( x ) < 0 for every real number x . Solution: Let f be a quadratic function defined by f ( x ) = a x 2 + b x + c , where a ≠ 0 Differentiating both sides with respect to x , we get f ′ ( x ) = 2 a x +

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ISBN: 9781464151088

Author: Associate Professor Laura Taalman, Peter Kohn

Publisher: W.H. Freeman & Company

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Chapter 3.3, Problem 93P

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To prove: Every quadratic function is either always concave up or always concave down.

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Chapter 3.3, Problem 92P

Chapter 3.3, Problem 94P

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To prove: Every quadratic function is either always concave up or always concave down.

Solution Summary: The author explains that every quadratic function is either always concave up or always converge down.

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To prove: Every quadratic function is either always concave up or always concave down.

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