A) \[8.00\]
B) \[5.25\]
C) \[4.00\]
D) \[6.25\]
Correct Answer: D
Solution :
Given, \[a=4,\,n=9,\,f(x)=\sqrt{x}\] and \[f(b)-f(a)=(b-a)\,f'(c)\] \[\Rightarrow \] \[f'(c)=\frac{f(b)-f(a)}{b-a}=\frac{3-2}{9-4}\] \[\Rightarrow \] \[f'(c)=\frac{1}{5}\] \[\Rightarrow \] \[\frac{1}{2}{{c}^{-1/2}}=\frac{1}{5}\] \[\Rightarrow \] \[{{c}^{-1/2}}=\frac{5}{2}\] \[\Rightarrow \] \[c={{\left( \frac{5}{2} \right)}^{2}}=\frac{25}{4}=6.25\]
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