A) 0
B) \[\frac{1}{2}\]
C) 2
D) 1
Correct Answer: D
Solution :
\[\left| f(x)-f(y) \right|\le 2{{\left| x-y \right|}^{3/2}}\] |
Dive both by \[\left| x-y \right|\] |
\[\left| \frac{f(x)-f(y)}{x-y} \right|\le 2.{{\left| x-y \right|}^{1/2}}\] |
Apply limit \[x\to y\] |
\[\left| f'(y) \right|\le 0\] |
\[\Rightarrow \] \[f'(y)=0\] \[\Rightarrow \] \[f(y)=c\] \[\Rightarrow \] \[f(x)=1\] |
\[\int\limits_{0}^{1}{1.dx=1.}\] |
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