Question

which of the statement is true Continuous function is always differentiable
O 0
Differentiable function is always continuous
0 There is no relation
O Both Chice 1 and 2 are correct​

Answer 1

Answer:

differentiable function is always continuous

Answer 2

Differentiable function is always continuous but not all continuous functions are differentiable.

Step-by-step explanation:

Differentiability is when the slope of the tangent line is equals to the limit of the function at a given point. This means  that if f is differentiable,then f'(c) exists, then it directly means that f is continuous at c.

Let us understand this with the help of an example.

Consider a function f(x)=|x|

The graph for this function has been attached.

In this graph , we see that the function is continuous, however, we see that the slope in the right hand side is +1 while the slope of the function in left hand side is -1.Therefore f(x) is not differentiable at x=0.

This means that f(x)=|x| is a continuous function but not differentiable.

Hence we leave the discussion with two important statements:

1. For a differentiable function, the function must be a continuous function as well.

2. For a continuous function, the function may not be a differentiable function.

Therefore the option: Differentiable function is always continuous is the correct option.