Question

Suppose that f is continuous on [a,b]. Is it necessary that there is a point where exist f' ?

Answer 1

not really, example |x| is not diff at x = 0

Answer 2

[a,b] might be a vertical line; does f' exist on vertical line?

Answer 3

but there is a point (ex. x = 1/2) where f' exist for f(x) = |x|

Answer 4

vertical line is not continuous function.

Answer 5

so what i mean that its not necessary

Answer 6

vertical lines arent functions

Answer 7

You are very polite with vertical line)

Answer 8

kanwar i answered your question and feel really good about it