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Question

The point on the curve y=x2+7x+2 closest to the line y=3x3 is

A
(2,8)
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B
(8,2)
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C
(2,8)
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D
(8,2)
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Solution

The correct option is A (2,8)
Let P(x,y) be a point on the curve
y=x2+7x+2
3x3=x2+7x+2
f(x)=x2+4x+5
f(x)=2x+4
For maxima or minima,
f(x)=0
x=2
f′′(x)=2>0
Hence,f(x) has a minimum at x=2
y=8
Hence, the point is (-2,-8).

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