Question

show that the function f(x) is differentiable at x= -3 where f(x) x2+2​

Answer 1

Answer:

We can rewrite f(x) as ,

f(x) = x-3 for x≥3

= 3-x for x<3

LHL of f(x) at x=3 is 0.

RHL of f(x) at x=3 is 0.

So, f(x) is continuous at x=3.

RHD of f(x) at x=3 , lim

h→0

{

3+h−3

(3+h)−3−(3−3)

}=1

LHD of f(x) at x=3 ,lim

h→0

{

3−h−3

3−(3−h)−(3−3)

}=−1

So, f(x) is not differentiable at x=3.

Answer 2

Answer:

x=-3

put the value of x in f(x)

(-3)^2+2

9+2

11