NDA2016MathematicsContinuity and DifferentiabilityActual
Consider the function f ( x )=| x -1|+ x ^2 , where x R . Which one of the following statements is correct?
Options
- Af ( x ) is continuous but not differentiable at x =0
- Bf(x) is continuous but not differentiable at x=1
- Cf ( x ) is differentiable at x =1
- Df ( x ) is not differentiable at x =0 and x =1
Correct answer
B. f(x) is continuous but not differentiable at x=1
Step-by-step solution
aligned & f(x)=|x-1|+x^2 x R & f₁(x)=|x-1|, f₂(x)=x^2 aligned f₁(x) and f₂(x) both are continuous. Hence f(x) is continuous. f(x) in differentiable at x=0f₁(x) is not differentiable at x=1 . Hence f(x) is continuous but not differentiable at x=1 .