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Humberto thinks the second derivative has something to do with how well a tangent line will approximate a curve. For example, he is comparing two functions, and , and he notices that at a certain , and . However, the second derivatives are different, and . Which tangent line gives a better approximation of its actual function near ? Use a graph to justify your answer. .

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Click the link at right for the full version of the eTool: Calc 6-136 HW eTool