Which of the following statements is true for the function f(x) = {x² + 3, x ≠ 0; 1, x = 0} ?

Question

MCQ (Single)Continuity of a Function at a PointDifferentiability and ContinuityCBSE PYQ

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Check whether the function f(x) = x² |x| is differentiable at x = 0 or not.

If y = √(tan √x), prove that √x (dy/dx) = (1 + y⁴)/(4y).

Differentiability and Continuity

The number of points of discontinuity of f(x) = {|x|+3, if x ≤ –3; –2x, if –3 < x < 3; 6x+2, if x ≥ 3} is :

A function f(x) = |1 – x + |x|| is :

If x = e^(x/y), prove that dy/dx = (log x – 1)/(log x)²

Check the differentiability of f(x) = {x² + 1, 0 ≤ x < 1; 3 – x, 1 ≤ x ≤ 2} at x = 1.