Consider the following statements: 1. f'(2+0) does not exist. 2. f'(2-0) does not exist. Which of the above statements is/are correct? [NDA I 2014]

Correct Answer is : Neither 1 nor 2

Correct Answer is : Neither 1 nor 2

Test Index

NDA Math Limit, Continuity and Differentiability

For the next three (03) items that follow:

Let f(x) be a function in

1\le x < \infty

f(x)=\begin{cases} 2-x & \text{for } 1\le x\le 2 \\ 3x-x^2 & \text{for } x>2 \end{cases}

[NDA I 2014]

Question : 101 of 105

Marks: +1, -0

f'(2+0)

f'(2-0)

Solution:

\text{L.H.L} = \lim\limits_{x \to 2^{-}} f(x) = 0

\text{R.H.L} = \lim\limits_{x \to 2^{+}} f(x) = 2

L.H.L ≠ R.H.L

f(x)

not differentiable at

x=2

,therefore not continuous.

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