A rectangle with its base on the x-axis is inscribed in a quadratic curve y=-x^2+12. Find the dimension of the rectangle if its area is a maximum.
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一題Differentiation-optimization
2009-10-08 5:04 am
回答 (1)
2009-10-08 5:21 am
✔ 最佳答案
Let the base be 2x (from -x to +x) where x is positiveThe height = y = 12 - x^2
The area A = 2x(12 - x^2) = 24x - 2x^3
dA / dx = 24 - 6x^2
dA / dx = 0 => x = 2
d^2A/dx^2 = -12x = -24 => maximum
x = 2 => height = 12 - 4 = 8
Therefore dimension of rectangle is 4 x 8
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