Calculus


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How can i tell if a function is differentiable, I've read the book and have no idea how:

"we say a function f is differentiable on tan interaval of the form [a,b],[a, +infinity),(- infinity, b], [a,b),or (a,b] if f is differentiable at all numbers inside the interval, and it is differentiable at the endpoint(s) form the left or right, as appropriate derivatives from the left and right."

make any sense to you guys?

Thanks.

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ive been outta high school for a week now :D yay and it's been a loong time since i've had calc class... but if i remember correctly (and anyone feel free to correct me, it's been a while) but if you graph the function and there's an asymptote if it has a bound of infinity (lower or upper) then it's differentiable.. i know that on a ti-89 you can graph the function and then if there's a definite lower and upper bound you goto calc>integrate and enter the bounds and if it gives you the integral then it's differentiable.. if it sits and cant come up w/ anything then it isnt

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How can i tell if a function is differentiable, I've read the book and have no idea how:

"we say a function f is differentiable on tan interaval of the form [a,b],[a, +infinity),(- infinity, b], [a,b),or (a,b] if f is differentiable at all numbers inside the interval, and it is differentiable at the endpoint(s) form the left or right, as appropriate derivatives from the left and right."

make any sense to you guys?

Thanks.

The book means "a function is differentiable on an interval if all points on that interval have a derivative." You can tell if a function is differentiable on an interval if the domain of the derivative of the function includes the interval.

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hmmm i have to be able to explain it on the test.  Don't think my teacher will take that for an answer  :pinch:

lol sorry.. i tried the best i could.. good luck on the test anyhow.. i always loved those calc tests :D

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Yeah, I've been outta school for a week also. Here is how it goes:

A derivative is basically the slop of the equation. So if the slope at a point does not exist (ie: it is a vertical line) then you cannot derivate it. Graphically, this point would be represented by a vertical asymptote or a "sharp turn."

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How can i tell if a function is differentiable

Actually, to answer your very first question, the answer is simple: a function f is differentiable if the domain of its derivative df/dx is all real numbers. If you don't know how to find the derivative of a function yet, post here again and I'll give a definition that doesn't involve derivatives.

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I dont know if this helps but it is differential until it becomes 0, you can keep taking higher order's of derivatives until you get a constant which is zero.

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Continous does not imply differentiable but it must be continous to be differentiable, even if piecewise.

So might as well look at the definition of a derivative, we realize that lim h+ nand lim h- must exist and be equal.

I haven't looked at this concept for quite a while since i took multivariate last summer and i believe this holds true even for partial derivatives.

All polynomials are differentiable. That's usually an easy one though. stuff like 1/x is not differentiable guess where ;)

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