Extreme Values(Continuation of Exercise 13.)a.Graph over

QUESTION:

Problem 14PE

Extreme Values

(Continuation of Exercise 13.)

a.Graph  over the interval .Where does the graph appear to have local extreme values or points of inflection?

b. Show that ƒ has a local maximum value at and a local minimum value at

c. Zoom in to find a viewing window that shows the presence of the extreme values at

Reference: Exercise 13

A graph that is large enough to show a function’s global behavior may fail to reveal important local features. The graph of  is a case in point.

a. Graph ƒ over the interval .Where does the graph appear to have local extreme values or points of inflection?

b. Now factor and local minima at

c. Zoom in on the graph to find a viewing window that shows the presence of the extreme values at

The moral here is that without calculus the existence of two of the three extreme values would probably have gone unnoticed. On any normal graph of the function, the values would lie close enough together to fall within the dimensions of a single pixel on the screen.