Question

Find the dimensions of the rectangle of largest area that has its base on the x-axis and its other two vertices above the x-axis and lying on the parabola.
y=5-x^2

Answer 1

length of rectange is represented as 2x, where x is x_value of point on parabola
width is represented as y, y_value of point on parabola

Area = 2x*y = 2x(5-x^2) = 10x -2x^3
maximize Area by finding x value where derivative is zero

dA/dx = 10 -6x^2 = 0
--> x = sqrt(5/3)

optimal dimensions:
length = 2sqrt(5/3)
width = 10/3

Answer 2

thank you