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Second Derivatives and Beyond

Second Derivatives and Beyond

Exercises

Page (12 of 12) Exercises:   1    2    3    4    5    6    7    8    9    10    11    12  

Exercise 12

These questions deal with characteristics of the first and second derivatives of a function at and near a maximum value.

a. Below is a graph of a function f with a maximum at x = x0. Determine the sign of the derivative f' at each labelled x-value.

b. Assume f is defined and twice differentiable on the whole real line. Around a maximum of the function f, is f concave up or concave down?

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