A given functiony = f(x)can be continuous or not continuous over its domain of real numbers. Further, the function may or may not be differentiable at points in its domain. If a function is differentiable at a point or interval in its domain, it...
We do not propose to give anything like a complete description of its history. Our goal will be to trace the general features of a single idea: the change in the view of mathematicians on the relationship between a function and its derivative from certainty as to the existence of a ...
Show that every differentiable function is continuous (converse is not true i.e., a function may be continuous but not differentiable). . Ans: Hint: Here we will use the basic definition of the differential function. Then we will form the conditio...
The functionf:R→Rgiven byf(x)=−|x−1|is (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 ...
The graph of the function f is shown below. Determine the interval where f is continuous but __not__ differentiable. Explain why the function is discontinuous at the given function number a. Sketch the graph of the function f(x) = \left\{\begin{matrix} \f...
The left-hand derivative and the right-hand derivative are not equal. Therefore, f(x) is not differentiable at x=4. Conclusion The function f(x)=|x−4| is continuous at x=4 but not differentiable at that point. --- Show More ...
] denotes the greatest integer function. Then View Solution Q5 If fx=loge|x|, then (a) f (x) is continuous and differentiable for all x in its domain (b) f (x) is continuous for all for all × in its domain but not differentiable at x = ± 1 (c) f (x) is neither ...
 CONSTRUCTION OF SOME KIESSWETTER-LIKE FUNCTIONS-THE CONTINUOUS BUT NON-DIFFERENT-IABLE FUNCTION DEFINED BY QUINARY DECIMAL[J]. Analysis in Theory and Applications. 2004(01)T. Yong and Y. Guangjun. Construction of some kiesswetter-like functions-the continuous but non-different-iable function...
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A function f(x) is differentiable in and f' is continuous in .Use Fundamental Theorem of Calculus to evaluate:a) f'b) f' 相关知识点: 试题来源: 解析 a) b) 反馈 收藏