Question

how can you tell if a function is continuous and differentiable ? Looking for quick answer

Answer 1

There is no quick way to know, other than from experience. Basically, you have to know the definitions, and analyze the function in question.

Answer 2

the only quick way, I suppose, is knowing from experience.

Answer 3

for example x / (2-x) would that be continuous or differentiable ?

Answer 4

can you tell just by looking at it ?

Answer 5

We can see it is continuous since lim x->a is equal to f(a). Differentiability at a point requires f'(a) exist. Does it for this function ?

Answer 6

a is 2 right ?

Answer 7

thats what you are refering a to ?

Answer 8

'a' can be any number in the domain.

Answer 9

yes so you took the 2 from the function right ?

Answer 10

i mean 2 from the function would equal a ?

Answer 11

2 from the function? you mean the 2 in: x/(2-x) ?

Answer 12

yes it would be plugged in for a ?

Answer 13

No. The number 'a' is a value of x. So if f(x) = x/(2-x), then f(a) = a/(2-a). Note, if a =2, then a would not be in the domain since f is not defined at x = 2.

Answer 14

hey are you there ? i just graphed x/(2-x) and it wasn't continuous

Answer 15

It is continuous over its domain (no holes, and no truncated points)

Answer 16

no according to the graph it isn't continous it starts at another direction that isn't continuity right ?

Answer 17

look http://www.math24.net/discontinuous-functions.html

Answer 18

I see. Yes, there is an asymptote at x = 2, which means the function is not continuous at that point, but it is also not defined there. At all other points, f is continuous and differentiable.

Answer 19

Okay thanks for clarifying!