For a function y=f(x), if the left-hand derivative f′(a−)and the right-hand derivative f′(a+) are equal at a point, the function is said to be differentiable at that point. The limit-definition of derivative of f(x) is as follows: ...
Learn about differentiability. Understand how to tell if a function is differentiable and when it isn't and see a comparison of differentiable vs. continuous. Related to this Question How to prove there is no lower bound for a continuously differentiable function?
these points will lie infinitesimally close together; therefore, it is the slope of the function in the pointx.Important to note is that this limit does not necessarily exist. If it does,
The condition number is the ratio of the change in output for a change in input in the ‘worst-case’—that is to say, at the point when the change in output is largest per given change in input. If a function is differentiable and in just one variable, the condition number can be ...
Vocabulary and Formula for Finding General Solutions to Differential Equations Involving Exponential Decay Exponential growth and decay model: If y is a differentiable function of t and its differential equation is in the form of dydt=ky, then: y=Cekt Where C is the initial valu...
If a function f is continuous on the closed interval [a, b], where a < b, and differentiable on the open interval (a, b), then there exists a point c in (a, b) such that the mean value therorem is true. No condition that f(a) and f(b) have to be equal. Hope this helps...
Let g(x) and h(y) be differentiable functions, and let f(x, y) = h(y)i+ g(x)j. Can f have a potential F(x, y)? If so, find it. You may assume that F would be smooth. (Hint: Consider the mixed partial derivatives of F.) How to answer this question? Wha...
A function is not differentiable if it has a cusp or sharp corner. As well as the problems with division by zero shown above, we can’t even findlimitsnear the cusp or corner because theslopeto the left of the cusp is different than the slope to the right. ...
It appears only to accept integer input. (It uses factorial, for example.) So it is NOT differentiable. fmincon will NOT work, nor will any tool that assumes smoothness in any form.What is the objective function (the thing that you are trying to maximize)...
I am trying to explain to someone the formal notion of a limit of a function, however it has made me realize that I might have some faults in my own understanding. I will write down how I understand the subject and would very much appreciate if someone(s) can point out any errors/...