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JEE Main20264 April 2026Morning ShiftMathematicsContinuity and DifferentiabilityActual

The number of points, at which the function f(x) = 6x, 2 + 3x^2 + |x - 1| | |x^2 - 1 4 | | , x (- , ) , is not differentiable, is _____.

Correct answer

0

Step-by-step solution

Let f(x) = g(x) + h(x) , where g(x) = 6x, 2 + 3x^2 h(x) = |x - 1| | |x^2 - 1 4 | | We find the points of non-differentiability of each part in x (- , ) . Non-differentiability of g(x) : g(x) = 6x, 2 + 3x^2 is non-differentiable where the two curves intersect with different slopes. 6x = 2 + 3x^2 3x^2 - 6x + 2 = 0 x = 6 36 - 24 6 = 6 2 3 6 = 1 1 3 Both values lie in (- , ) . At these points, the derivatives of the two inner functions are 6 and 6x ; since x 1 , the slopes differ. So g(x) contributes 2 points. Non-diff

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