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The rectangle located in the first quadrant and is basically inscribed under a decreasing curve.The lower left hand corner is at the origin and the upper right hand corner on the curve. the equation is y = 5-2x^2.Please find the width, height and area of the largest such rectangle.

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Hint: If $(x,y)$ is the upper corner of the rectangle, you have $A=xy$. Substitute in your equation for $y$ to get $A$ as a function of $x$. Then take $\frac {dA}{dx}$ and set it to zero to get an equation in $x$.

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  • $\begingroup$ Im not sure what to do from there. would the answer be -4 $\endgroup$ – Michael Rametta Mar 27 '13 at 1:04
  • $\begingroup$ @MichaelRametta: what do you get for $\frac {dA}{dx}$? I get $x$ close to $+1$ and an area about 3 $\endgroup$ – Ross Millikan Mar 27 '13 at 1:43
  • $\begingroup$ I am still confused can you please help me $\endgroup$ – Michael Rametta Mar 27 '13 at 2:54
  • $\begingroup$ @MichaelRametta: only if you show what you have tried. I don't know where you are confused. I gave a process, what steps can you do and what can you not? $\endgroup$ – Ross Millikan Mar 27 '13 at 3:05
  • $\begingroup$ and so A' (x) = 0 when x=1/2 $\endgroup$ – Michael Rametta Mar 27 '13 at 3:19

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