When is fx differentiable

Moritz Moritz 33 3 3 bronze badges. I think I should tell you that the correct answer had a in front of the -2 in the first interval and not a [.

In other words, the interval looked like this: -2, Regardless, thank you! Remember— differentiable is a subcategory of continuous.

Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password. Post as a guest Name. Email Required, but never shown. Upcoming Events. Featured on Meta. Now live: A fully responsive profile. The unofficial elections nomination post. A differentiable function is always continuous but every continuous function is not differentiable. In this article, we will explore the meaning of differentiable, how to use differentiability rules to find if the function is differentiable, understand the importance of limits in differentiability, and discover other interesting aspects of it.

A function is said to be differentiable if the derivative of the function exists at all points in its domain. Let us look at some examples of polynomial and transcendental functions that are differentiable:.

If f, g are differentiable functions, then we can use some rules to determine the derivatives of their sum, difference, product and quotient. Here are some differentiability formulas used to find the derivatives of a differentiable function:. In calculus, differentiation of differentiable functions is a mathematical process of determining the rate of change of the functions with respect to the variable.

Some common differentiability formulas that we use to solve various mathematical problems are:. There is an alternative way to determine if a function f x is differentiable using the limits.

Let's see the behavior of the function as h becomes closer to 0 from the negative x - axis. What happens when h approaches 0 from right? Now, let's see the behavior of the function as h becomes closer to 0 from the positive x - axis.

We say that a function is continuous at a point if its graph is unbroken at that point. A differentiable function is always a continuous function but a continuous function is not necessarily differentiable.

A function is formally considered differentiable if its derivative exists at each point in its domain, but what does this mean? So, as long as you can evaluate the derivative at every point on the curve, the function is differentiable. Hence, differentiability is when the slope of the tangent line equals the limit of the function at a given point. This directly suggests that for a function to be differentiable, it must be continuous, and its derivative must be continuous as well. Now, this leads us to some very important implications — all differentiable functions must therefore be continuous, but not all continuous functions are differentiable!

Simply put, differentiable means the derivative exists at every point in its domain. Consequently, the only way for the derivative to exist is if the function also exists i.