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

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 ...

Let $f: mathbb{R}^n o mathbb{R}$ be a $C^3$ function. Have $x_0$ be a
critical point of $f$. How would I go about proving that if the
quadratic form $q(h)$ corresponding to $f$ at $x_0$ is ...

Context: I just completed the first quarter of an Intro to Real
Analysis class, and while I was thinking about how some functions
(like $x^2$) aren't uniformly continuous because they, roughly ...

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 ...

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 ...

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-} ...