Question

inter 1 year maths 1b Chapter 9 Differentiation Exercise 9a ​

Answer 1

No, the following function is not differential at 2.

1) We have,

f(x) = x if x lies between 0 and 2

f(x)=2 if x is greater than 2.

Graph of f(x) is as attached as shown in figure.

2) At x=2-,

f(x)=2

At x=2+,

f(x) = 2

Hence, At x=2 , function is continuous.

3) Now, For differentiation

For x<=2,

$f'(2-) = 1$

For x>2,

$f'(2+)=0$

In short, $f'(2-) \neq f'(2+)$

Hence, Function is not derivable at x=2.