Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA2016MathematicsContinuity and DifferentiabilityActual

Paragraph: Let f(x)=[|x|-|x-1|]^2 Question: What is f ^ ( x ) equal to when 0 x 1 ?

Options

  1. A0
  2. B2 x-1
  3. C4 x-2
  4. D8 x-4

Correct answer

D. 8 x-4

Step-by-step solution

Given f(x)=(|x|-|x+1|)^2f(x)= array cc 1 & x 0 (2 x-1)^2 & 0 x 1 1 & x 1 array . When 0 x 1 aligned & f(x)=(2 x-1)^2 & f^ (x)=2(2 x-1) 2=4(2 x-1) & f^ (x)=8 x-4 aligned

Practice Continuity and Differentiability on Quantrex Academy →

More from Continuity and Differentiability

What is the derivative of x |x| with respect to x , where x<0 ? 2026Passage: Let f(x)= cases ax(x-1), & x 3 cases Given that f(x) is continuous for all x but not differentiable at x=1 . Further f'(x) is continuous at x=3 . Question: What is the val 2026Passage: Let f(x)= (x^2) and g(x)=x|x| for |x| Question: If q(x)=f g(x) , then which of the following statements is/are correct ? I. q(x) is continuous at x=0 . II. q(x) is differe 2026Passage: Let f(x)= (x^2) and g(x)=x|x| for |x| Question: If p(x)=f(x)g(x) , then which of the following statements is/are correct ? I. p(x) is continuous at x=0 . II. p(x) is diffe 2026If f(x) is differentiable at x=a , then consider the following statements : I. f(x) is continuous at x=a II. _ x a f(x)=f(a) Which of the statements given above is/are correct ? 2026Passage: Let f(x)= cases ax(x-1), & x 3 cases Given that f(x) is continuous for all x but not differentiable at x=1 . Further f'(x) is continuous at x=3 . Question: What is the val 2026Consider the following for the two (02) items that follow: Let f(x) = cases x^3, & x^2 What is _ x 0 f'(x) equal to? 2025For the following two (02) items: Let the function f(x) = |x - 3| + |x - 4| be defined on the interval [0, 5] . What is dy dx at x = 3.5 equal to? 2025 Full Continuity and Differentiability list All NDA PYQs