Sep 20, 2015 · 1 Generally, setting the two different pieces of the piecewise function equal to each other and setting their derivatives equal is a good shortcut and will usually yield the correct answer. …

Oct 10, 2017 · Find the values of a and b that makes the following function differentiable Ask Question Asked 8 years, 6 months ago Modified 3 years, 4 months ago

3 A function is differentiable (has a derivative) at point x if the following limit exists: $$ \lim_ {h\to 0} \frac {f (x+h)-f (x)} {h} $$ The first definition is equivalent to this one (because for this limit to exist, the two …

A function is "differentiable" if it has a derivative. A function is "continuous" if it has no sudden jumps in it. Until today, I thought these were merely two equivalent definitions of the same c...

Aug 21, 2022 · The existence of partial derivatives doesn't make the function nice enough as differentiability in one dimension. Take into account that you are only probing two directions out of …

May 15, 2017 · What does it mean for the derivative of a function to exist at every point on the function's domain? It seems a very abstract thing to visualize. Can someone elaborate? Answers are much …

Jun 3, 2023 · I understand that for every x≠1 the function is differentiable. and now I'm trying the find the values of 'a' and 'b' that make the function differentiable at x=e

1 Generally, if you graph a piecewise function and at any point it doesn't look "smooth" (there's a "sharp" turn), then it is not differentiable at that point. More rigorously, the derivatives of the two parts of the …

Dec 4, 2024 · A point $c$ is an inflection point (whether $f$ is differentiable at $c$ or not) if the function is convex on some interval $ (a,c)$ and concave on some interval $ (c,b)$ or vice versa.

Jan 17, 2023 · Suppose f is a differentiable function. It can be shown that the set of points of discontinuity of f' must be a meagre, F- $\sigma$ set. A theorem from Lebesgue says that a function …