Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET20227 Jul 2022Evening ShiftMathematicsContinuity and DifferentiabilityActual

f(x)= array lc 4 & ,- < x < - 5 x^2-1, & - 5 < x 5 4, & 5 x < array . If k is the number of points where f(x) is not differentiable, then k-2=

Options

  1. A2
  2. B1
  3. C0
  4. D3

Correct answer

C. 0

Step-by-step solution

Points to check, x=- 5 , x= 5 f(x)= array l 4,- < x < - 5 x^2-1,- 5 x 5 4, 5 x < array . At x=- 5 , LHL = RHL =f(- 5 )=4 LHD =0, RHD =2(- 5 )=-2 5 LHD RHD Not differentiable at x=-: 5 At x= 5 LHD =2 5 , RHD =0 Not differentiable at x= 5 k=2, k-2=0

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