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 , t

Question

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

TestHub · Accepted Answer

Let W = n w ⇒ d t d W ​ = n d t d w ​ + w ⋅ d t d n ​ Given : w = t 2 − t + 2 and n = 2 t 2 + 3 ⇒ d t d w ​ = 2 t − 1 and d t d n ​ = 4 t ∴ Equation (1) ⇒ d t d w ​ = ( 2 t 2 + 3 ) ( 2 t − 1 ) + ( t 2 − t + 2 ) ( 4 t ) Thus, d t d W ​ ​ t = 1 ​ = ( 2 + 3 ) ( 2 − 1 ) + ( 2 ) ( 4 ) = 5 ( 1 ) + 8 = 13

Mathematics - Application of Derivative Question with Solution | TestHub

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