Some Max-Min Problems

Problem #1:

Find the dimensions of the rectangle of perimeter P that has the largest area. See Applet #1

Problem #2:

A ball is thrown straight up, with an initial speed of 64 feet per second, from a cliff 96 feet above the ground.

1. Where is the ball t seconds later?
2. When it reach its maximum height?
3. How hight above the ground does the ball rise?
4. When does the ball hit the ground?

Assume that there is no air resistance and that the accelaration due to the gravity is constant. See Applet #2

Problem #3:

Find the coordinates of P that maximize the area of the rectangle shown in the figure below. See Applet #3

Problem #4:

The base of a triangle is on the x-axis, one side lies along the line y = 3x, and the third side passes through the point (1,1). What is the slope of the third side if the area of the triangle is to be a minimm? See Applet #4  

Problem #5:

A triangle is formed by the coordinate axes and a line through the point (2,5) as in the figure below. Determine the slope of this line if the area of the triangle is to be a minimum.

In the setting of the previous exercise determine the slope of the line if the area is to be a maximum. See Applet #5