A) \[\frac{13}{4}\]
B) \[\frac{17}{4}\]
C) \[\frac{21}{4}\]
D) \[\frac{23}{4}\]
E) \[\frac{25}{4}\]
Correct Answer: E
Solution :
Function\[f(x)=\sqrt{x}\]and\[[4,\text{ }9]\] Here,\[a=4\]and\[b=9\] \[f(a)=f(4)=2\]and \[f(b)=f(9)=3\] By Lagranges mean value theorem, \[\Rightarrow \] \[\frac{f(b)-f(a)}{b-a}=f(x)\] \[\Rightarrow \] \[\frac{3-2}{9-4}=\frac{1}{2\sqrt{x}}\] \[\Rightarrow \] \[\frac{1}{2\sqrt{x}}=\frac{1}{5}\] \[\Rightarrow \] \[x=\frac{25}{4}\] Which lies in the given interval\[[4,\text{ }9]\].
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