Question

- Optimization problem -
A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola . What are the dimensions of such a rectangle with the greatest possible area?

Answer 1

oh sorry the parabola is y=5-x^2

Answer 2

I was thinking find the 0 for the parabola, and because it touches the 2 upper part I get sqrt(5) and -sqrt(5) being the length for y and I can ind the length in x because those 2 y are the distance between 2 cornor that is the length?

Answer 3

Since the rectangular inscribed in the parabola:
it's length is symmetry x+ x
=> A = 2x y
= 2x ( 5 - x²)

Answer 4

oh. inscribed in, so i had it wrong... so you don't have any constraint in this problem...?

Answer 5

I think the range of parabola is the constraint, just get the concept first!

Answer 6

Well I usually go about these problem by finding my constraint then the equation I need to solve, but I couldn't do so.

But when you say A=x(5-x^2) and so I take the derivative of both side and I should get
x(5-2x) + (5-x^2) = A'(x)
5x-2x^2+5-x^2
-3x^2+5x+5 and then use quadratic to find my x ?

Answer 7

A = 2x ( 5 - x²)
= -2x³ + 10x
->A' = -6x² + 10 = 0 => x = √ 5/3

Answer 8

but wait, why did you mention x + x being symmetrical? and I asked about the constraint because, don't you need one to do an optimization problem?

Answer 9

Did you sketch the rectangular inscribes in the parabola, you'll see the constraint
-√ 5 ≤ x ≤ √5, 0 ≤ y ≤ 5