# Thread: Maximum & Minimum Problem

1. ## Maximum & Minimum Problem

What is the maximum possible area of a rectangle with base that lies on the x-axis and with two upper vertices that lie on the graph of the equation $\displaystyle y$$\displaystyle =$$\displaystyle 4$$\displaystyle -$$\displaystyle x^2$?

I have no idea how to do this, can someone please show the full solutions to help me through the process? Thank you!!!

2. Originally Posted by bhuang
What is the maximum possible area of a rectangle with base that lies on the x-axis and with two upper vertices that lie on the graph of the equation $\displaystyle y$$\displaystyle =$$\displaystyle 4$$\displaystyle -$$\displaystyle x^2$?

I have no idea how to do this, can someone please show the full solutions to help me through the process? Thank you!!!
Start by drawing a picture (did you do that?). Let the coordinates of the vertices have x-coordinates at x = a and x = -a. Get an expression for the area in terms of a. Then use calculus in the usual way to maximise this area.