17. If a function f(x) is differentiable at x =c, prove that it is continuous at x = c. 相关知识点: 试题来源: 解析Since fis differentiable atc. we have i lim_(x→c)(f(x)-f(c))/(x-c)=f'(c) But for, we have x≠qc f(x)-f(x)=(f(x)-f(c))/(x-c)⋅(x-c)...
百度试题 结果1 题目f(x)xo If the function is differentiable at, the f(x)x___ C is continuous at.( ) A. 正确 B. 错误 相关知识点: 试题来源: 解析 A 反馈 收藏
Differentiable Functions:Suppose we have a function with input and output sets that are subsets of R, which is said to be differentiable at a point of its input set if the function has derivative at the point. When a function is differentiable in a subset of its domain ...
Consider the function f(x) = x*absolute of (x). A) Is f differentiable at x = 0? B) Is f continuous at x = 0? Is f(x) = (x^2 - 7) / (x - 3) continuous on the interval (3, infinity)? Consider the function f(x) = 4 + x2, if x greater than 1...
The correct Answer is:C To solve the problem, we need to analyze the function f(x) given the conditions provided. Let's break it down step by step. Step 1: Understand the Given InformationWe know that:- f(x) is continuous and differentiable on the interval (−7,0).- The derivative...
Rolle's Theorem If f(x) is continuous on [a, b], differentiable on (a, b), and f(a) = f(b), then there is guaranteed to exist a value of c on (a, b) such that f'(c) = 0.Consider the function, f(x), presented on the previous page. Does Rolle's Theorem apply on ...
If f is continuous for a≤q x≤q b and differentiable for a x b, which of the following could be false? ( ) A. f' ( c )= (f(b)-f(a))(b-a) for some c such that a c b. B. f' ( c )=0 for some c such that a c b. C. f has a minimum value on a≤q ...
Df(x) is differentiable only in a finite interval containing zero Submit Iff(x)=|x|+|x−1|, then which one of the following is correct? View Solution Iff(x)=|x−2|, where x is a real number, then, which one of the following is correct?
If f is continuous for all real numbers and ∫0216f(x)dx=600, find ∫06x2f(x3)dx. Hint: try using u-substitution. U-Substitution: One powerful yet simple method of integration is the technique of u-substitution. This method performs a...
Here we will assume that the function is increasing in the interval (a,b). Now, we have the continuous function is the interval {eq}[a,b] {/eq} So...Become a member and unlock all Study Answers Start today. Try it now Create an account...