Asked by Brit
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
Answered by
Reiny
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
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.