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: ...
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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,
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? Wh...
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 ...
Types of Functions: How To Know if It’s a Function Thevertical line testis a simple way to figure out if you have a function. You could also use to “many to one” rule: Is a function: “many to one“. This is saying if you have multiple x-values that map to one y-value —...
Is it because its square of error does not contribute much to the SSE minimization? If so, how do I modify the objective function to get a local minimum that also fits well with the concentrations that are of the 1E-02 magnitude? I have followed the htt...
This is the general solution of the given differential equation. 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 th...
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)...
is never exactly equal to L), just a value arbitrarily close to L?! PeroK said: All I'd add is that if that limit does not exist at some point x0x_0 then ff is not differentiable at x0x_0. And, such functions do exist! Good point, I had meant to put that in my ...