Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y= 3-x^2. What are the dimensions of such a rectangle with the greatest possible area?
My Solution:
Okay, I understand I have to find a rectangle with the greatest size that has to corners in f(x) = 3-x^2. But I really do not know how to even start, would someone please give me a hint?
Start at the origin. Call the length from the origin going directly along the x-axis to the end of the rectangle "x". Thus if you went the other way along the x-axis you would go another distance of "x", and the total length of the base is "2x". Now since the upper corners are on the graph of, that's a give away that your height can now be given by
, which gives you an area function of
. Now differentiate and set the derivative equal to zero to find the critical point(s). And once you get you critical x-value, plug that into your area function and you should have your answer.
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