5. Find all values of x for which h has relative maximum or minimum values. Explain your results.

Students may investigate extreme values by plotting the derivative of the function. Since the function is smooth, its extreme values occur when the derivative is zero.

Input := 

Plot[h'[x], {x, -10, 10}]

Output =

-Graphics-

From the graph of f'[x] it appears that the only root is at x = 0. Due to the nature of the function, we must use Find Root rather that the Solve command.

Input := 

FindRoot[h'[x]==0, {x, 0}]

Output =

{x -> 0.}