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

 xguru 25/12/2015 9:47 am HOME » 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-} ...

 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-} ... TAGS: Check Function Differentiable Point math stackexchange 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 ... TAGS: differentiable function always integrable math stackexchange 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 ... TAGS: check derivative implicit function correct math 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 ... TAGS: quadratic form corresponding function critical point 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 ... TAGS: necessary that limit exists point should What is the "fastest" increasing function that's useful in some area of math? – math.stackexchange.com 17/12/2014 1:05 pm by google-app-engine 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 ... TAGS: What fastest increasing function that useful 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 self-studying 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, ... TAGS: What does removing point have with 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 ... TAGS: point Fundamental Theorem Calculus math stackexchange Does a continuous point-wise 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. ... TAGS: Does continuous point wise limit imply 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? TAGS: Does triangle always have point where