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

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 ...

How can I check if my derivative for an implicit function is correct? – math.stackexchange.com 
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 
8/12/2014 1:05 am by undeinpirat in Development 

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 ...

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 ...

What is the "fastest" increasing function that's useful in some area of math? – math.stackexchange.com 
17/12/2014 1:05 pm by googleappengine in Development 

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 ...

What does "removing a point" have to do with homeomorphisms? – math.stackexchange.com 
17/12/2014 7:05 pm by Edo in Development 

I am selfstudying topology from Munkres. One exercise asks, in part,
to show that the spaces $(0,1)$ and $(0,1]$ are not homeomorphic. An
apparent solution is as follows: If you remove a point, ...

Don't see the point of the Fundamental Theorem of Calculus. – math.stackexchange.com 
11/12/2014 7:05 am by bdurbin in Development 

$$frac{d}{dx}int_a^xf(t)dt$$
I would love to to understand what exactly is the point of FTC. I'm
not interested in mechanically churning out solutions to problems.
It doesn't state anything ...

Does a continuous pointwise limit imply uniform convergence? – math.stackexchange.com 
16/11/2014 10:05 am by beefjerky911 in Development 

Question
Given a sequence of continuous functions $(f_n)_{n in mathbb N}$ and
define
$$
f : X
ightarrow Y, quad f(x) = lim_{n
ightarrow infty} f_n(x)
$$
where $X$ and $Y$ are metric spaces.
...

Does a triangle always have a point where each side subtends equal 120º angles? – math.stackexchange.com 
3/12/2014 10:05 am by Nulq in Development 

Is there a point $O$ inside a triangle $ riangle ABC$ (any triangle)
such that the angle $angle{AOB} = angle{BOC} = angle{AOC}$?
What do we call this point?
