A) 32
B) \[\frac{32}{3}\]
C) \[\frac{32}{9}\]
D) None of these
Correct Answer: C
Solution :
We have \[F(x)=\frac{1}{{{x}^{2}}}\int_{4}^{x}{(4{{t}^{2}}-2F'(t))dt}\] \[\therefore \,\,F'(x)=\frac{1}{{{x}^{2}}}\left( 4{{x}^{2}}-2F'(x) \right)-\frac{2}{{{x}^{3}}}\int_{4}^{x}{(4{{t}^{2}}-2F'(t))dt}\] Þ \[F'(4)=\frac{1}{16}[64-2F'(4)]-0\Rightarrow F'(4)=\frac{32}{9}\].You need to login to perform this action.
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