I. Use the graphing calculator to graph each function on the interval indicated. Use the notation from the MATH and TEST menus.

Sketch a picture of what appears on your screen. Locate the extreme points on the pictures and label them as maxima or minima. Use the definitions of maxima and minima to explain how you identified the points indicated, if such exists.

1. y=-x^2+4x-1; I=[0,3]
2. y=(1/5)(2x^3+3x^2-12x); I=[-3,3]
3. y=x^3-3x+1; I=(-3/2,3) Hint: Watch out, this one is not a closed interval.
4. y=1/(1+x^2) ; I=[-2,1]
5. y=x^(2/5) ; I=[-1,32]

II. Identify what was common to the functions which had both a maximum and minimum point and what was common to the others. Explain how this relates to the theorems we are studying.

III. For each of the functions that had an extreme point, find F'(x). Explain the relationship between the extreme points that occurred in the interiors of the intervals and F'(x) in each case. If an extreme point was not in the interior, where was it? Explain how your findings relate to the theorems we are studying.

IV. Find all of the extreme values for each function. Show the algebra and calculus work that backs up your answers. Explain the procedure you would use to find the extreme values for a function without using a graph.