Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Manipal MET2015MathematicsContinuity and Differentiability

If f(x)= 1, x^2, x^3 , then

Options

  1. Af(x) is not everywhere continuous
  2. Bf(x) is continuous and differentiable everywhere
  3. Cf(x) is not differentiable at two points
  4. Df(x) is not differentiable at one point

Correct answer

D. f(x) is not differentiable at one point

Step-by-step solution

It is evident from the graph of f(x) that f(x)= array cc 1, & x 1 x^3, & x 1 array . Clearly, f(x) is everywhere continuous but it is not differentiable at x=1 .

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 Manipal MET PYQs