Oct 10, 2017 · Find the values of a and b that makes the following function differentiable Ask Question Asked 8 years ago Modified 2 years, 11 months ago

A function is differentiable at a point, $x_0$, if it can be approximated very close to $x_0$ by $f (x)=a_0+a_1 (x-x_0)$. That is, up close, the function looks like a straight line.

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 …

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? …

How exactly would I be able to get the values to be differentiable? I know that the point at 2 has to exist and that it has to be continuous and connect to the other function to work.

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 …

Moreover, there are functions which are continuous but nowhere differentiable, such as the Weierstrass function. On the other hand, continuity follows from differentiability, so there are …

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...

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 …

Jan 5, 2017 · 1 Since we need to prove that the function is differentiable everywhere, in other words, we are proving that the derivative of the function is defined everywhere. In the given …