Question

A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y=7-x^2 .

What are the dimensions of such a rectangle with the greatest possible area?

Answer 1

if the base is on the x-axis, the width of the rectangle is = x
if the height is based on the parabola, the length = 7-x^2

the area of a rectangle = length * width

thus, area = x*(7-x^2)
= 7x-x^3

in order to maximize the area, you would need to take the derivative of the area and set it equal to 0

Area = 7x-x^3
Area' = 7 - 3x^2

7-3x^2 = 0
thus, x = 1.5275

this x represents the x needed to create the largest possible area with the given parameters.

Thus:
Width (x-axis) = 1.5275
Length (y-axis) = 7 - (1.5275)^2 = 4.6667

hope this helps

Answer 2

ohhh okay i see thanks for the step by step

Answer 3

no worries :)