SOLUTION: **Solve using calculus optimization** Find the point on the curve {{{ y=x^2 }}} that is closest to the point (18, 0).

SOLUTION: Solve using calculus optimization Find the point on the curve {{{ y=x^2 }}} that is closest to the point (18, 0).

Question 1142727: **Solve using calculus optimization**
Find the point on the curve that is closest to the point (18, 0).
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Find the point on the curve that is closest to the point (18, 0).
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The points on the curve are (x,x^2)
The distance d(x) to (18,0) is
d(x) =
d'(x) = (1/2)*(4x^3 + 2x - 36)/sqrt(...) = 0
2x^3 + x - 18 = 0
x = 2
===============
The point is (2,4)
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The distance is sqrt(16^2 + 4^2) = 4sqrt(17) units.

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