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Question

A point on the curve y=x2+x, where the tangent is parallel to the chord joining the points (0, 0) and (1, 2) is .

A
(12,34)
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B
(14,32)
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C
(34,32)
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D
(12,54)
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Solution

The correct option is A (12,34)
According to Lagrange's Mean Value theorem, for a curve f(x), the tangent at point (c, f(c)) is parallel to chord joining the points (a, f(a)) and (b, f(b)) where, point c is given by f'(c)=f(b)−f(a)b−aNow, f(x)=x2+x ⇒f'(x)=2x+1∴2c+1=2−01−0=2⇒c=12f(12)=(12)2+12=34∴The required point is (12,34).

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