Second Derivatives and Beyond
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?