# Second Derivatives and Beyond

### Exercises

#### Exercise 11

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

a. Below is a graph of a function *f* with a minimum at *x* = x_{0}. 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 minimum of the function *f*, is *f* concave up or concave down?

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