If we have the statement "If a function is continuous, it is differentiable", and we know a function is not differentiable, then A. it is continuous B. it is not continuous C. we can't determine D. the statement is invalid 相关知识点: ...
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...
(a) continuous as well as differentiable at x = 1 (b) not continuous but differentiable at x = 1 (c) continous but not differentiable at x = 1 (d) neither continous nor differentiable at x = 1 View Solution Letf(x)=|x|. Then, for allxfis continuous (b)fis differentiable for som...
Answer to: If f(x) and f (x) are continuous, differentiable functions that satisfy f(x)=x^3+4x^2 \leq \int_0^x (x t)f (t) \text{d}t...
Let f(x)={1, x <= -1, |x|, -1 < x < 1, 0, x >=1 . Then, f is (a) continuous at x=-1 (b) differentiable at x=-1 (c) everywhere continuous (d) everywhere differentiable View Solution Doubtnut is No.1 Study App and Learning App with Instant Video Solutions for NCERT ...
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 ...
结果1 题目 Let f be continuous on [a,b] and differentiable on (a,b). If there exists c in (a,b) such that f'(c)=0, does it follow that f(a)=f(b)? Explain. 相关知识点: 试题来源: 解析 No. Let f(x)=x^2 on [-1,2]. 反馈 收藏 ...
For a function to be continuous we have to have:L=f(c). We can easily prove that if a function is differentiable then it is continuous. From here we have that if a function isn't continuous it is differentiable. Answer and ...
If fx=11+e1/x,x≠00,x=0 then f (x) is (a) continuous as well as differentiable at x = 0 (b) continuous but not differentiable at x = 0 (c) differentiable but not continuous at x = 0 (d) none of these Solution (d) none of these we have, (LHLatx=0)=limx→0-f(x)=...
Consider the function f(x) = x*absolute of (x). A) Is f differentiable at x = 0? B) Is f continuous at x = 0? Find all the values of x where the following function is continuous: f(x) = \dfrac{x + 2}{x - 4}.