How to check if function is continuous and differentiable? Show that the function, f(x) = \left\{\begin{matrix} (x^2 + 1), & if & x \leq -1\-2x, & if & x > -1 \end{matrix}\right. is continuous and differentiable at the value x = -1. ...
is differentiable How? Differentiability: A function f(x) defined in the closed interval [a,b] is said to be differentiable if its derivative function is also continuous in the open interval (a,b) Hence to check whether a function is different...
Afunctionthat has a continuous derivative isdifferentiable; It’s derivative is acontinuous function. How do I know if I have a continuous derivative? As the definition of a continuous derivative includes the fact that the derivative must be a continuous function, you’ll have tocheck for contin...
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? W...
aTaylor ' s Theorem, which will be introduced in this section, is a basic theorem to show how to approximate a given differentiable function by means of polynomials which has important applications in theoretical research and approximate calculations. 泰勒‘s定理,在这个部分将被介绍,是显示如何的一...
Therefore, y = |x| is sometimes called the “absolute value parent function.” Check with your particular author (or your instructor) to make sure you know which terminology they are using.Absolute Value Parent FunctionAn absolute value function has a unique “V” shape when plotted on a ...
A function is uniformly differentiable if its derivative is uniformly continuous? 2 If f(x)f(x) is a continously differentiable function such that f′(x)f′(x) is unbounded, then f(x)f(x) is not unifromly continuous? 0 Proving that a differentiable function f, with f' ...
This error makes sense sincetorch.gefunction is not differentiable. However, sinceMaxPool2Dis also not differentiable, I believe that there are ways of mitigating non-differentiability in PyTorch. It would be great if someone could point me to any source which can help me eith...
forhto 0, 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 function is differentiable; if it does not, then the function is not differentiable. ...
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: ...