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Homework Statement
A rectangle has one vertex in quadrant I at the point (x,y) which lies on the graph of y = 2x^2 and another vertex at the point (-x, y) in the second quadrant and the other vertices on the x-axis at (-x, 0) and (x, 0)
What is the domain of the area function?
y = 2x^2 = w
l = 2x
Vertices:
(-x, 0)
(x,0)
(-x,y)
(x,y)
Homework Equations
2x(2x^2) = 4x^3
2x = 2x^2
The Attempt at a Solution
Find the zeros:
0
Find the maximum area:
1
[0,1] is the domain
But I am not so sure about this. On the one hand a rectangle can't have infinite area. On the other hand, 4x^3, the area function goes all the way to infinity.
So am I approaching this wrong? How do I find the maximum area if the function has no max? I know that x cannot be any lower than 0 since that would mean negative area and negative area only applies in integral calculus.
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