Question 1107690: The point P(x, y) lies on the parabola y=(1/2)x^2. Find this point such that the sum S of the abscissa and ordinate is a minimum. Found 2 solutions by stanbon, ikleyn:Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! The point P(x, y) lies on the parabola y=(1/2)x^2. Find this point such that the sum S of the abscissa and ordinate is a minimum.
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Sum of x and (1/2)x^2 = (1/2)x^2+x
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Mimimum occurs where x = -b/(2a) = -1/(2) = -1/2-Then y = (1/2)(1/2)^2 -(1/2) = (1/2)(1/4)-(1/2) = (1/8)-(1/2) = (2-8)/16 = -3/8
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Minimum sum = (-1/2)+(-3/8) = (-4/8)+(-3/8) = -7/8
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Cheers,
Stan H.
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You can put this solution on YOUR website! .
The point P(x, y) lies on the parabola y=(1/2)x^2. Find this point such that the sum S of the abscissa and ordinate is a minimum.
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Sum of x and (1/2)x^2 = (1/2)x^2+x.
Mimimum of this quadratic function occurs where
x = - = - = -1.
Then y = = .
Minimum sum = .
Answer. Minimum sum = .
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