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 differentiable or not, just find the derivative...
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: ...
The first way of calculating the derivative of a function is by simply calculating the limit. If it exists, then you have the derivative, or else you know the function is not differentiable. Example As a function, we takef(x) = x2. (f(x+h)-f(x))/h = ((x+h)2- x2)/h = ...
Find the slope of the graph of the function f(x)=x(2x^4+4) at x=5.\Describe the x-values at which the graph of the function f(x)=\frac{x^2}{x^2-9} is differentiable. Describe the graph of the equation: 49...
agood night, miss saturday 晚上好,错过星期六 [translate] aJt (x0, x ) is a concave homogeneous differentiable function Jt (x0, x)是一个凹面同类的可微函数 [translate] aI hate you!your is bendan and shagua 我恨您! 您是bendan和shagua [translate] aIn addition,I have another question ...
Differentiable or Non-Differentiable 1. Domain and Range The set of all inputs (e.g., x-values) is called thedomain. For example, the f(x) = x2can have any number as an x-value, so the domain is (-∞, ∞). Therangeis the set of all outputs (e.g., y-values). ...
Solutions withx(0)≠0x(0)≠0will havex′(0)=12x′(0)=12, but should curve upwards very quickly to avoid intersecting the above solution. Such a quick turn might be missed if the step size is too large, so numerical solutions may cross, contrary to the behavior of t...
The absolute value parent function.The absolute value parent function is written as: f(x) = │x│ where:f(x) = x if x > 0 0 if x = 0 -x if x < 0As the definition has three pieces, this is also a type of piecewise function. It’s only true that the absolute value function...
There is a hint given for this problem:Use the Fundamental Theorem of Calculus to show that f(x+h)−f(x)−Dhf(x)=∫10Dhf(x+sh)−Dhf(x)dsf(x+h)−f(x)−Dhf(x)=∫01Dhf(x+sh)−Dhf(x)dsSome initial thoughts:I need to show that f is both (totally) diffe...
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...