I really need help on this problem. I have no idea how to do this.:
A rectangle is inscribed in the region enclosed by the graphs of F(x)=18-x^2 and G(x)= 2x^2- 9. It gives a picture too, but there are no points on it for the rectangle. The rectangle is vertical though, with the longest legs being parallel to the Y axis, and the shortest to the X axis.
A. Find the height of the rectangle as a function of X.
B. Find the Width of the rectangle in terms of X.
c. Write the area of the rectangle as a function of X.
I think this has to do with optimization. But how would you find the max area of a shape in parabolas if you didn't have the points of where the rectangle intersected the parabola? I've already found the vertex points of the parabolas: ) (0, 19) and 0, -9. But does that even have anything to do with the problem? I'm so freakin' confused.