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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?

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lublana

Answer with Step-by-step explanation:

We are given that

[tex]f(x)=\mid x-9\mid[/tex]

[tex]f(x)=-(x-9)[/tex] when x<9

[tex]f(x)=x-9[/tex] when [tex]x\geq 9[/tex]

LHD

[tex]\lim_{x\rightarrow 9-}f'(x)[/tex]

=[tex]-\lim_{x\rightarrow 9-}(x-9)=-1[/tex]

RHD

[tex]\lim_{x\rightarrow 9+}f'(x)[/tex]

[tex]=\lim_{x\rightarrow 9+}(x-9)=1[/tex]

[tex]LHD\neq RHD[/tex]

Hence, the function is not differentiable at x=9

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