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  4. A function is said to be differentiable in an interval [a, b], if it is differentiable at every point of [a, b]

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Q. A function is said to be differentiable in an interval $[a, b]$, if it is differentiable at every point of $[a, b]$

Continuity and Differentiability

Solution:

A function is said to be differentiable in an interval $[a, b]$ if it is differentiable at every point of $[a, b]$. As in case of continuity, at the end point $a$ and $b$, we take the right hand limit and left hand limit which are nothing but left hand derivative and right hand derivative of the function at $a$ and $b$ respectively.