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...
Determine whether the statement, if a function is differentiable at point (a,f(a)), then f(x) is continuous at x=a, is true or false. Differentiable Functions: Let's say we have a function y=f(x). If the function is continuous a...
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: ...
Define continuity and differentiability of a function at a point verify the continuity and differentiability of the function: ,f(x)=⎧⎪⎨⎪⎩(1−x)x<1(1−x)(2−x)1≤x≤2(3−x)x>2⎞⎟⎠ View Solution Iff(x)={x,x≤1,x2+bx+c,x>1''f∈dbandciffunctioniscont...
1Let f be a function such that f(x)=f(1-x) for all real numbers x.If f is differentiable everywhere,then f'(0)=?为什么是-f'(1)而不是f'(1)? 2 Let f be a function such that f(x)=f(1-x) for all real numbers x.If f is differentiable everywhere,then f'(0)=? 为什么是...
a,b] and differentiable on the open interval (a,b), which of the following theorems mightnot be satisfied?I. Mean Value TheoremII. Rolle's TheoremIII. Extreme Value TheoremA:III, onlyB:II, onlyC:I, onlyD:II andIII, only 相关知识点: ...
Similar Questions Iff(x)is a twice differentiable function such thatf(0)=f(1)=f(2)=0. Then View Solution Free Ncert Solutions English Medium NCERT Solutions NCERT Solutions for Class 12 English Medium NCERT Solutions for Class 11 English Medium ...
doi:10.2139/ssrn.2892746exact Taylor’s expansionapproximationUsing a new approach, we provide new Taylor expansions when the original function is not differentiable.Alghalith, MoawiaSocial Science Electronic Publishing
A function f(x) and interval [a,b] are given. Check if Rolle's Theorem can be applied to f on [a,b]; if so, find c in [a,b] such that f' (c)=0. f(x)=6 on [−1,1]. Rolle's Theorem:...
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 x...