A helicopter is flying along the curve $y = x^{2} + 2$ . A soldier is placed at the point $(3, 2)$ , find the nearest distance between the soldier and helicopter.

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Solution

Let the point on $y = x^{2} + 2$ be $(h, h^{2} + 2)$
Distance $d = \sqrt{(h - 3)^{2} + (h^{2})^{2}}$
$d^{2} = (h - 3)^{2} + (h)^{4}$
$d^{'} = 0 ⟹ 2 h^{3} + h - 3 = 0 ⟹ h = 1$
$d_{m i n} = \sqrt{(1 - 3)^{2} + (1)^{4}} = \sqrt{5}$

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A helicopter is flying along the curve y=x2+2. A soldier is placed at the point (3,2), find the nearest distance between the soldier and helicopter.

Let the point on y=x2+2 be (h,h2+2)Distance d=√(h−3)2+(h2)2 d2=(h−3)2+(h)4d′=0⟹2h3+h−3=0⟹h=1dmin=√(1−3)2+(1)4=√5

A helicopter is flying along the curve $y = x^{2} + 2$ . A soldier is placed at the point $(3, 2)$ , find the nearest distance between the soldier and helicopter.

Let the point on $y = x^{2} + 2$ be $(h, h^{2} + 2)$
Distance $d = \sqrt{(h - 3)^{2} + (h^{2})^{2}}$
$d^{2} = (h - 3)^{2} + (h)^{4}$
$d^{'} = 0 ⟹ 2 h^{3} + h - 3 = 0 ⟹ h = 1$
$d_{m i n} = \sqrt{(1 - 3)^{2} + (1)^{4}} = \sqrt{5}$