MCQ
In the interval $(0, 1)$ maximum value of the function $f (x) = |x\ ln\ x|$ is
- A$0$
- B$1$
- C$e$
- ✓$e^{-1}$
✓
Answer
Correct option: D.
$e^{-1}$
d
$f(x)=-x \ln x$
$f(x)=-x \ln x$
$f^{\prime}(x)=-1-\ln x$
$\therefore f'(x) > 0{\rm{ if }}x \in (0,1/c)$
$f^{\prime}(x)=0 \text { if } x=1 / e$
$f^{\prime}(x)<0 \text { if } x>1 / e$
$f(1 / e)=e^{-1}$
${\rm{ \,and\, }}\mathop {\lim }\limits_{x \to {0^ + }} f(x) - 0{\rm{ \,and\, }}\mathop {\lim }\limits_{x \to {1^ - }} f(x) = 0$
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