If $F\left( x \right) = \frac{1}{{{x^2}}}\mathop \smallint \limits_4^x \left( {4{t^2} - 2F'\left( t \right)} \right)dt$ , then $F'\left( 4 \right)$ equals

JEE MATHEMATICS MCQ: DIFFERENTIATION

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Analyzing +4 | -1

F\left( x \right) = \frac{1}{{{x^2}}}\int \limits_4^x \left( {4{t^2} - 2F'\left( t \right)} \right)dt

, then

F'\left( 4 \right)

equals

View answer and explanation

Correct option: A

\frac{{32}}{9}

Option A (

\frac{{32}}{9}

) is correct because after differentiating both sides and substituting x=4, we find that F'(4) =

\frac{{32}}{9}

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