Question
A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y=6–x^2. What are the dimensions of such a rectangle with the greatest possible area?
Find Width=____ & Height=4
just need to find width.. is not 2
Find Width=____ & Height=4
just need to find width.. is not 2
Answers
let the point of contact be (x,y)
then the base is 2x and the height is y
area = 2xy = 2x(6-x^2) = 12x - 2x^3
d(area)/dx = 12 - 6x^2
= 0 for a max of area
6x^2 = 12
x^2 = 2
x = √2, then y = 6-2 = 4
rectangle has a base of 2√2 and a height of 4
then the base is 2x and the height is y
area = 2xy = 2x(6-x^2) = 12x - 2x^3
d(area)/dx = 12 - 6x^2
= 0 for a max of area
6x^2 = 12
x^2 = 2
x = √2, then y = 6-2 = 4
rectangle has a base of 2√2 and a height of 4