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 o
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...
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 ...
In an explicit function, one variable is defined completely in terms of the other. The general form is:y = f(x), for a < x < b
Vocabulary and Formula for Finding Particular Solutions to Differential Equations Involving Exponential Decay Exponential Growth or Decay Model:If {eq}y {/eq} is a differentiable function of {eq}t {/eq} and its differential equation is in the form of {eq}\frac{\mathrm {d...
"lsqcurvefit" itself applies to a special case of "lsqnonlin" when the residual vector has the form r(x)= F(x,xdata)-ydata Conversely, lsqnonlin can be applied to any (differentiable) residual function r(x). In our case, since we want to apply a "weig...
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)...
One possibility is to use ANNs to obtain an approximate solution to the value function of the HJB equation24,26. An alternative method is based on the solution of Pontryagin’s maximum principle via differentiable programming27. Control approaches that rely on Pontryagin’s maximum principle ...