MCQ
Rolle's theorem is applicable in case of $\phi(\text{x})=\text{a}^{\sin\text{x}},\text{a}>\text{a}$ in :
- AAny interval.
- ✓Any interval $[0,\pi]$
- CAny interval $\Big[0,\frac{\pi}{2}\Big]$
- DNone of these.
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$1.$ Which of the following is true for $0 < x < 1$ ?
$(A)$ $0 < $ f(x) $ < \infty$
$(B)$ $-\frac{1}{2} < f(x) < \frac{1}{2}$
$(C)$ $-\frac{1}{4} < f(x) < 1$
$(D)$ $-\infty < $ f $($ x $) < 0$
$2.$ If the function $e^{-x} f(x)$ assumes its minimum in the interval $[0,1]$ at $x=\frac{1}{4}$, which of the following is true?
$(A)$ $f^{\prime}(x)$
$(B)$ $f^{\prime}(x)>f(x), 0$
$(C)$ f $^{\prime}(x)$
$(D)$ $f^{\prime}(x)$
Give the answer question $1$ and $2.$
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