Equation of Tangent at a Point (x,y) in Terms of f'(x)
If ‘P’ be a p...
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
(√3,√34)
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C
(−√3,−√34)
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D
(1,1)
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Solution
The correct option is A (0, 0) dydx=1−x2(1+x2)2⇒d2ydx2=2x(x2−3)(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)=1−3(1+3)2=−18
Thus x = 0 is the required point.