Sports car racing is a form of motorsport which uses sports car prototypes. The competition is held on special tracks designed in various shapes. The equation of one such track is given as follows: f(x) = { x⁴ − 4x² + 4, 0 ≤ x < 3 { x² + 40, x ≥ 3 Based on given information, answer the following questions:

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Derivative of a Function, Continuity of a Function at a Point, Differentiability and Continuity | PadhAiPro

Question

CASE_STUDIESDerivative of a FunctionContinuity of a Function at a PointDifferentiability and Continuity4 sub-questions

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

The derivative of sin (x²) w.r.t. x, at x = √π is :

Derivative of a Function

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).

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 :

The derivative of tan⁻¹(x²) w.r.t. x is :