SOLUTION: 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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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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Answer by ikleyn(52903)   (Show Source): You can put this solution on YOUR website!
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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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Any other answer is incorrect.


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