Check if a Function is Differentiable at a Point – math.stackexchange.com


xguru
25/12/2015 9:47 am
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Let $$f(x)= egin{cases} x+1 & xleq0 \ 3^{-x} & x>0 end{cases}$$ Is the function differentiable at $x=0$? I should look at the limits $$lim_{h o 0-} ...

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Check if a Function is Differentiable at a Point – math.stackexchange.com
25/12/2015 9:47 am by xguru in Development
Let $$f(x)= egin{cases} x+1 & xleq0 \ 3^{-x} & x>0 end{cases}$$ Is the function differentiable at $x=0$? I should look at the limits $$lim_{h o 0-} ...
Is a differentiable function always integrable? – math.stackexchange.com
29/11/2014 1:05 am by Vijayant Singh in Development
So my question is, say I have a function that is differentiable on $(-2, 4)$. Is it always integrable on $[-2, 4]$? I know that if $f$ is diff on $(-2, 4)$, then it is continuous on $(-2, 4)$. And I ...
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24/12/2014 1:05 pm by ioudas in Development
For explicit functions I can calculate the derivative at a certian point using the original function: $$frac{f(1+0.1) - f(1)}{0.1}$$ And then use $frac{d}{dx}f(1)$ to check if the function is ...
quadratic form corresponding to function at critical point is positive definite implies local minimum – math.stackexchange.com
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Is it necessary that if a limit exists at a point it should be also defined at that point? – math.stackexchange.com
17/11/2015 1:44 pm by zclin in Development
Say there exists a limit $lim_{x o x_0}f(x) = L$. Is it necessary that $f$ be defined at the point $x_0$ itself? Well, what I think of it is that it's OK to be undefined at that point because I ...
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