what is the relation between differentiability and continuity?

Answer 1

differentiable functions are a subset of continuous ones. For example:

y=3 for x<=3
y=x for x>3

... is continuous but not differentiable (it has no slope at x=3).

Answer 2

A function is continuous if there are no 'jumps' or sudden impluses in the function over an interval. A function is differentiable, typically, if the function is continuous over the interval. Some discontinuous functions are still differentiable, but the topic is a bit more advanced.
Traditionally, differentiability is a consequence of continuity.

Answer 3

A function f(x) which is defined at all points in yhe neighborhood of x= a is said to be continuous for x = a if if the following three conditions are satisfied: (a) f(a) exists, (b) lim f(x) as x --> a exists, and (c) lim f(x) as x --> a = f(a). A function is said to be continuous in an interval if it is continuous at every point in that interval.

If a function f(x) is differentiable for all values of x in a given interval, then f(x) is continuous in that interval. It is possible for a function f(x) to be continuous in an interval and yet not be differentiable for any value of x in that interval. Such functions are not met in elememtary calculus.

Answer 4

For something to be differentiable, it must be continuous.

Answer 5

one relation could be
for a function to be diffrentiable ,it must be continous
but converse is not true