Need help with differentiablility

1. Oct 17, 2009

noname1

Last edited: Oct 17, 2009
2. Oct 17, 2009

Staff: Mentor

Your question doesn't make much sense the way it's written, or maybe I don't understand what you're trying to say.

I'm assuming that m and n are real numbers.

nx + m is differentiable for any values of m and n, regardless of the value of x. If the domain is restricted to x <= -1, it's still differentiable.

nx3 +x + 2m is differentiable for all values of m and n, regardless of the value of x.

It occurs to me that what you have, but didn't explain very well, is a function whose formula is different on the two intervals. If that's the case, you want to find m and n so that
$$1) \lim_{x \rightarrow -1^-} f(x)~=~\lim_{x \rightarrow -1^+} f(x)$$
$$2) \lim_{x \rightarrow -1^+} f'(x)~=~\lim_{x \rightarrow -1^+} f'(x)$$
If the first condition is satisfied, your function will be continuous for all x. If the second is satisfied, the derivative will be continuous for all x.

3. Oct 17, 2009

noname1

that how the question is written

i have to find the value of n and m that will make them differentiable, i solve the first one and it give me m = -1+n,

than i do limit from the right side is equal to the left resolve it and n = 1

than i replace n from the initial equation and than gives me 0, is this correct?