Home › AP EAPCET (Engineering) › Mathematics › Continuity and Differentiability › The function f(x) = |x| at x = 0 is
The function f(x) = |x| at x = 0 is
Aboth continuous and differentiable
Bneither continuous nor differentiable
Cdifferentiable but not continuous
Dcontinuous but not differentiable
Answer & Solution
Correct answer: D. continuous but not differentiable
The graph has no break at 0, but the left slope is -1 and the right slope is +1, so no derivative exists.
Related questions
The identity x = e^(log x) holds only forThe function f(x) = 1/(x - 2) is discontinuous atThe greatest integer function [x] is discontinuous at which of these points?For x > 0, logarithmic differentiation shows that the derivative of x^x isIf x^2 + y^2 = 1, implicit differentiation gives dy/dx equal toLet f(x) = kx^2 for x <= 2 and f(x) = 3 for x > 2. For continuity at x = 2, the value of kA function equals (x^2 - 9)/(x - 3) for x not equal to 3 and has value k at x = 3. It is cTaking natural logs of y = [u(x)]^v(x) gives log y equal to