A rectangle with sides on the x-axis and y-axis has its upper vertex in the first quadrant at the point (x,f(x)) on the graph of F(x)=24-3x-x^2. Find the maximum possible area of the rectangle.

Question

kainui · Answer

The area of the rectangle is what you're maximizing, so that means you're going to need a formula for area of the rectangle. Try making one and I'll help guide you along. =D

kainui · Answer

Try graphing the function on your calculator and then draw a picture of a rectangle on your paper and see if that helps.

anonymous · Answer

The area of the rectangle would be: A=x*y right? Would I take the derivative of the function next?

anonymous · Answer

We aren't allowed to use calculators so I'm trying to do it by hand as much as possible

kainui · Answer

True, calculators won't be allowed, but you should be able to know it's an upside down parabola from -x^2 term. Picture drawing is allowed and strongly encouraged as it gives you something to work with.|dw:1355306438847:dw|

You're right, A=xy, however when you maximize you can't take the derivative with respect to both x and y at the same time. So what you must do is plug in for x or y, generally which ever is easiest.