Where is the following function differentiable

Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. How to determine whether this function is differentiable at a point? Ask Question. Asked 6 years, 1 month ago. Active 1 year, 9 months ago. Viewed k times. F of three, we already evaluated this. This is going to be nine. And let's see if we can evaluate this limit, or let's see what the limit is as we approach from the left hand side or the right hand side, and if they are approaching the same thing then that same thing that they are approaching is a limit.

So let's first think about the limit as x approaches three from the left hand side. So it's over x minus three, and we have f of x minus nine. But as we approach from the left hand side, this is f of x, as x is less than three, f of x is equal to x squared. So this would be instead of f of x minus 9 I'll write x squared minus nine, and x squared minus nine. This is a difference of squares, so this is x plus three times x minus three, x plus three times x minus three.

And so these would cancel out. We can say that is equivalent to x plus three as long as x does not equal three. That's okay because we're approaching from the left, and as we approach from the left x plus three is defined for all real numbers, it's continuous for all real numbers, so we can just substitute the three in there. So we would get a six. So now let's try to evaluate the limit as we approach from the right hand side.

So once again it's f of x, but as we approach from the right hand side, f of x is six x minus nine. That's our f of x. And then we have minus f of three, which is nine. So it's six x minus Six x minus 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. Find the values of a and b that makes the following function differentiable Ask Question. Asked 4 years, 1 month ago.

Active 3 years, 6 months ago. Viewed 21k times. Future Math person. Future Math person Future Math person 2, 1 1 gold badge 15 15 silver badges 39 39 bronze badges. I know because i solved a bunch of these. And why do you need continuity in f' x again? Show 4 more comments.

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