Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA2013MathematicsContinuity and DifferentiabilityActual

Consider the function f(x)= array cc x^2, & x 2 3 x-2, & x 2 array . . Which one of the following statements is correct in respect of the above function?

Options

  1. Af(x) is derivable but not continuous at x=2 .
  2. Bf(x) is continuous but not derivable at x=2 .
  3. Cf(x) is neither continuous nor derivable at x=2 .
  4. Df(x) is continuous as well as derivable at x=2 .

Correct answer

B. f(x) is continuous but not derivable at x=2 .

Step-by-step solution

Let f(2+h)=4 as h 0 Let f(2-h)=4 as h 0 Let f(2)=4 continuous at x=2f^ (2⁺ )=4, f^ (2⁻ )=3

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