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Question

If ‘P’ be a point on the graph of y = x1 + x2 then co-ordinates of ‘P’ such that tangent drawn to the curve at ‘P’ has greatest slope in magnitude is

A
(0, 0)
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B
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C
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D
None of these
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Solution

The correct option is A (0, 0)
dydx=1x2(1+x2)2d2ydx2=2x(x23)(1+x2)3
Using the sign scheme for d2ydx2 we get that x = ±3 are the points of minima for f'(x), and x = 0 is the point of maxima for f'(x)
f'(0) = 1, f'(±3)=13(1+3)2=18
Thus x = 0 is the required point.

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