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Alex
3 years ago
7

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?
Mathematics
1 answer:
nydimaria [60]3 years ago
8 0

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

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