Question

Consider the following function. f(x) = |x − 9| Find the derivative from the left at x = 9. If it does not exist, enter NONE. -1 Correct: Your answer is correct. Find the derivative from the right at x = 9. If it does not exist, enter NONE. none Incorrect: Your answer is incorrect. Is the function differentiable at x = 9?

Answer 1

Answer with Step-by-step explanation:

We are given that

$f(x)=\mid x-9\mid$

$f(x)=-(x-9)$ when x<9

$f(x)=x-9$ when $x\geq 9$

LHD

$\lim_{x\rightarrow 9-}f'(x)$

=$-\lim_{x\rightarrow 9-}(x-9)=-1$

RHD

$\lim_{x\rightarrow 9+}f'(x)$

$=\lim_{x\rightarrow 9+}(x-9)=1$

$LHD\neq RHD$

Hence, the function is not differentiable at x=9