Question

why is it necessary to take the derivative of a continuous functions only?

Answer 1

because derivatives tell us the changes in slopes, where a function is discontinuous: the slope is undefined, so the change too is not useful--or even possible.

Answer 2

can you give me a mathematical example of it???

Answer 3

use the definition of a derivative if you have a discontinous function for say a limit... your limit is not defined

Answer 4

can't you proof it by any mathematical example?

Answer 5

this is one example why.

Answer 6

but x^2 is a continuous function?

Answer 7

\[\underbrace{x+x+x+\cdots+x}_{xtimes}\]isnt though. It makes sense to say "add five 5 times" or , "add three 3 times", but it doesnt make sense for .5 or sqrt 2. That function isnt continuous, it only works for integers. so taking derivatives doesnt make sense. As you can see, if we were able to take derivatives of it, we would end up with 1 = 2, or whatever nonsense you want to create.