Question

help please !!

Answer 1

well, differentiability means continuity

Answer 2

There can't be any breaks. cusps, or corners. the function wont be differentiable at that point.

Answer 3

so isnt there discontinuity ?

Answer 4

yes, well there is let me show you

Answer 5

Here is an example of a discontinuity see that circular hole there. the function isn't defined there so there won't be a derivative at that point.

Answer 6

o so that means continuity

Answer 7

well the function can be continuous everywhere, but except the points where you have breaks, cusps or corners

Answer 8

oh so then thats called discontinuity ?

Answer 9

yep

Answer 10

oh okay so differential relates to the x axis?

Answer 11

well, you mean differentiation in general?

Answer 12

yes

Answer 13

\[\frac{ dy }{ dx }\] just means the change in one variable with respect to another. it's just a fancy way of saying slope if that's what you mean. so when we mean differentiable it just means can we take the slope of the function at that point.

but if the function isn't defined or is discontinuous you can't find the slope/ derivative.

Answer 14

Another more fancy way of writing the derivative is this but don't worry about it. means the same thing just taking the slope.


\[\lim_{x \rightarrow 0}\frac{ f(x+h)-f(x) }{ h }\]

Answer 15

oh so whats the differnece when u have f prime (a)