A) \[5{{f}^{2}}(c)f'(c)\]
B) \[5f'(c)\]
C) \[f(c)f'(c)\]
D) None of these
Correct Answer: A
Solution :
[a] Let \[g(x)={{f}^{3}}(x)\] \[\Rightarrow g'(x)=3{{f}^{2}}(x)\cdot f'(x)\] \[\because f:[2,7]\to [0,\infty )\Rightarrow g:[2,7]\to [0,\infty )\] Using Lagrange?s mean value theorem on g(x), We get \[g'(c)=\frac{g(7)-g(2)}{5},c\in [2,\,7]\] \[\Rightarrow 2{{f}^{2}}(c)f'(c)=(f(7)-f(2))\] \[\frac{{{(f(7))}^{2}}+{{(f(2))}^{2}}+f(2)f(7)}{3}\]You need to login to perform this action.
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