Question

what is the height of the largest rectangle that can be drawn in a region bounded by the x axis and the graph of the following equation

Answer 1

\[y=\sqrt{4-x^2}\]

Answer 2

do you know how to find maxima of a function?

Answer 3

yea 2nd deriv right?

Answer 4

yes now can you tell me the shape of the function?

Answer 5

awesome!

Answer 6

thx :P

Answer 7

Now I want you to draw a random rectangle inside the semicircle with one side on the x axis and opposite vertices on the circumference. can you do that?

Answer 8

and please name the vertices.