Question

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

• A. including $a$ and $b$
• B. excluding $a$ and $b$
• C. including a but not $b$
• D. including $b$ but not $a$

Answer 1

Answer: (A)

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.