For each of the following, find an explicit formula for an example of a function satisfying the given properties. (a) A function f which has infinitely many local maximums, infinitely many local minimums, and no global extrema. (b) A function g which is continuous on ( - infinity, + infinity) where g is not differentiable at a point where it has a global extreme value. (c) A differentiable function h where every point is a critical point of h.

Sketch the graph of a function on the interval [-3,4] that has the given properties: • An absolute maximum at x = -2, but is not continuous at x = -2. • A local minimum at x = 1, but is not differentiable at x = 1. • Has a local maximum at x = 3, is continuous, and differentiable at x = 3. • Does not have an absolute minimum.

Sketch a SINGLE graph of a function f with all of the following properties, mark any point of inflections, local max and mins as well.

Find the absolute maxima and absolute minima of the function f(x) = = Answer: The absolute maximum occurs at x = The absolute minimum occurs at x = 3 -x2-3x-1 on [-7,9]. - with value f(x) = , with value f(x) =