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JEE Main2012MathematicsApplication of DerivativesActual

The weight W of a certain stock of fish is given by W=n w , where n is the size of stock and w is the average weight of a fish. If n and w change with time t as n=2 t^2+3 and w=t^2-t+2 , then the rate of change of W with respect to t at t=1 is

Options

  1. A1
  2. B8
  3. C13
  4. D5

Correct answer

C. 13

Step-by-step solution

Let W =n w d W d t =n d w d t +w d n d t Given : w=t^2-t+2 and n=2 t^2+3 d w d t =2 t-1 and d n d t =4 t Equation (1) d w d t = (2 t^2+3 )(2 t-1)+ (t^2-t+2 )(4 t) Thus, . d W d t |_ t=1 =(2+3)(2-1)+(2)(4) =5(1)+8=13

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