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: ...
Related to this Question How to prove there is no lower bound for a continuously differentiable function? How to show if function is differentiable? How to prove that a function is differentiable at a point? Suppose that y = f(x) is a differentiable function. Prove: \frac{df}{dx} \cdo...
Math: How to Find the Tangent Line of a Function in a Point Another application is finding extreme values of a function, so the (local) minimum or maximum of a function. Since in the minimum the function is at it lowest point, the slope goes from negative to positive. Therefore, the d...
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...
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 ...
What is a Critical Number? A critical number (or critical value) is a number “c” that is in the domain of the function and either: Makes the derivative equal to zero: f′(c) = 0, or Results in an undefined derivative (i.e. it’s not differentiable at that place): f′(c) ...
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 ...
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...