Question

Graphical Analysis Consider the functions f and g, where

and

(a) Use a graphing utility to graph f and g in the same viewing window.

(b) Explain why g is nonnegative.

(c) Identify the points on the graph of g that correspond to the extrema of f.

(d) Does each of the zeros of f correspond to an extremum of g? Explain.

(e) Consider the function

Use a graphing utility to graph h. What is the relationship between g and h? Verify your conjecture.