Most Important Selected Qs for JEE AdvancedMathematicsApplication of Derivatives

The point of inflection for the curve y= x+1 x^2+1 is

Options

A(-2- 3 , - 3 -1 4 )
B(-2+ 3 , -1- 3 4 )
C(-2+ 3 , 1+ 3 4 )
D(1,1)

Correct answer

D. (1,1)

Step-by-step solution

d y d x = -x^2-2 x+1 (x^2+1 )^2 and d^2 y d x^2 = 2 x^3+6 x^2-6 x-2 (x^2+1 )^3 d^2 y d x^2 is 0 at three points which are the roots of the equation x^3+3 x^2-3 x-1=0 i.e. -2- 3 ,-2+ 3 , 1 . Checking the sign of d^2 y d x^2 in the neighbourhood of these points, all these are the point of inflection.

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