Question

F(x)=∣x−3∣ A-Is the function f differentiable at x=3 ? Why? B-Find f′(2) and f′(5

Answer 1

The function is not differentiable at x=3

f'(2) = -1

f'(5) = 1

Explanation:

`f(x)=|x-3|\\\\f'(x)=(x-3)/(|x-3|)`

Since
`f'(3)` is undefined, then the function is not differentiable at x=3. However, we can determine
`f'(2)` and
`f'(5)`:

`f'(2)=(2-3)/(|2-3|)=(-1)/(|-1|)=-1\\\\f'(5)=(5-3)/(|5-3|)=(2)/(|2|)=1`