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

User Jan Omacka
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1 Answer

3 votes

Answer:

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

User Charles Zink
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