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Differentiability questions. Please solve . answer is 2 but left hand limit does not exist. How is it possible ?? (Question in attachment)

Differentiability questions. Please solve . answer is 2 but left hand limit does not exist. How is it possible ?? (Question in attachment)

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1 Answers

Aditya Gupta
2081 Points
4 years ago
the domain of the given function is [0, infinity).
so, by definition, it is said to be differentiable at each point in its domain if it is derivable everywhere in in (0, infinity) and the right hand derivative at 0 exists.
as you can see, the right hand derivative at zero exists and is equal to  – 1.
so, it is said to be differentiable at 0 just because of the definition of derivability at the end points of an interval.

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