AP EAMCET201920 Apr 2019Evening ShiftMathematicsContinuity and DifferentiabilityActual

The number of points in the interval (0,2) at which f(x)=|x-0.5|+|x-1|+ x is not differentiable is

Options

Correct answer

C. 3

Step-by-step solution

Given, f(x)=|x-0.5|+|x-1|+ x Clearly f(x) is not differentiable at x=0.5,1 and 2 for x (0,2) . Number of Non differentiable points of f(x) are 3 . Hence, option (c) is correct.

Practice Continuity and Differentiability on Quantrex Academy →

More from Continuity and Differentiability

The function f(x) = |x| + |x - 1| is: 2026 If f(x) = cases 1+x - 1-x x , & x 0 k, & x = 0 cases is continuous at x = 0 , then k = 2026 The function y = ||x| - 1| is differentiable for all values of ' x ' except 2026 Let f : R R be the function given by f(x) = |x - 2| + 3|x - 1| + ||x - 2| - 1| . What is the number of points where f is NOT differentiable? 2026 For real numbers a and b , consider the function f : R R given by f(x) = cases -ax - b & if x 1. cases How many pairs (a, b) are there for which f is continuous at every point of R 2026 If f(x) = cases ax + 7 & if x 1 cases is continuous at x = 1 , then 2026 If the function f(x) defined by f(x) = cases ax + 1 & if x 3 bx + 3 & if x > 3 cases is continuous at x = 3 , then (a - b) = .......... 2026 Let [x] denotes the greatest integer less than or equal to x and f(x) = [ ^2 x] , then which of the following is true ? 2026 Full Continuity and Differentiability list All AP EAMCET PYQs