A) \[f(4)<8\]
B) \[f(4)\ge 8\]
C) \[f(4)\ge 12\]
D) None of these
Correct Answer: B
Solution :
[b] By mean value theorem, there exists a real number \[c\in (2,4)\] such that \[f'(c)=\frac{f(4)-f(2)}{4-2}\Rightarrow f'(c)=\frac{f(4)+4}{2}\] Since, \[f'(c)\ge 6,\forall x\in [2,4]\] \[\therefore \,\,\,\,f'(c)\ge 6,\Rightarrow \frac{f(4)+4}{2}\ge 6\] \[\Rightarrow f(4)+4\ge 12\Rightarrow f(4)\ge 8\].You need to login to perform this action.
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