Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202522 May 2025Morning ShiftMathematicsContinuity and DifferentiabilityActual

Assertion (A) : If y=f(x)=(|x|-|x-1|)^2 , then ( d y d x )_ x=1 =1 Reason (R) : If _ x a f(x)-f(a) x-a exist, then it is called derivative of f ( x ) at x = a . Then

Options

  1. A(A) is true, (R) is true, (R) is correct explanation to (A)
  2. B(A) is true, (R) is true, (R) is not the correct explanation to (A)
  3. C(A) is true, (R) is false
  4. D(A) is false, (R) is true

Correct answer

D. (A) is false, (R) is true

Step-by-step solution

NO SOLUTION

Practice Continuity and Differentiability on Quantrex Academy →

More from Continuity and Differentiability

The function f(x) = |x| + |x - 1| is: 2026If f(x) = cases 1+x - 1-x x , & x 0 k, & x = 0 cases is continuous at x = 0 , then k = 2026The function y = ||x| - 1| is differentiable for all values of ' x ' except 2026Let 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? 2026For 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 2026If f(x) = cases ax + 7 & if x 1 cases is continuous at x = 1 , then 2026If 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) = .......... 2026Let [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