Rectangles beneath a parabola A rectangle is constructed with its base on 2 ? the ? -axis and two of its vertices on the par ? abola ?y =? 6 ? x , What are the dimensions of the rectangle with the maximum area? What is the area?

Solution Step 1: Let the length of rectangle be 2x And breadth of the rectangle be y Then area of the rectangle is given by A=2xy Step 2: We can draw the figure from the given data Step 3: The requirement of the rectangle lies on the graph of y=16 x 2 That is A=2x(16 x )2 A=32x-2x 3 ;0 x 4 The variable x is restricted between [0,4] at which both points yield a minimum value of no rectangle or 0 area