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MarcLeclair
 2 years ago
 Optimization problem 
A rectangle is inscribed with its base on the xaxis and its upper corners on the parabola . What are the dimensions of such a rectangle with the greatest possible area?
MarcLeclair
 2 years ago
 Optimization problem  A rectangle is inscribed with its base on the xaxis and its upper corners on the parabola . What are the dimensions of such a rectangle with the greatest possible area?

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MarcLeclair
 2 years ago
Best ResponseYou've already chosen the best response.0oh sorry the parabola is y=5x^2

MarcLeclair
 2 years ago
Best ResponseYou've already chosen the best response.0I 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?

Chlorophyll
 2 years ago
Best ResponseYou've already chosen the best response.1Since the rectangular inscribed in the parabola: it's length is symmetry x+ x => A = 2x y = 2x ( 5  x²)

MarcLeclair
 2 years ago
Best ResponseYou've already chosen the best response.0oh. inscribed in, so i had it wrong... so you don't have any constraint in this problem...?

Chlorophyll
 2 years ago
Best ResponseYou've already chosen the best response.1I think the range of parabola is the constraint, just get the concept first!

MarcLeclair
 2 years ago
Best ResponseYou've already chosen the best response.0Well 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(5x^2) and so I take the derivative of both side and I should get x(52x) + (5x^2) = A'(x) 5x2x^2+5x^2 3x^2+5x+5 and then use quadratic to find my x ?

Chlorophyll
 2 years ago
Best ResponseYou've already chosen the best response.1A = 2x ( 5  x²) = 2x³ + 10x >A' = 6x² + 10 = 0 => x = √ 5/3

MarcLeclair
 2 years ago
Best ResponseYou've already chosen the best response.0but 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?

Chlorophyll
 2 years ago
Best ResponseYou've already chosen the best response.1Did you sketch the rectangular inscribes in the parabola, you'll see the constraint √ 5 ≤ x ≤ √5, 0 ≤ y ≤ 5
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