Question
Mathematics Question on Application of derivatives
The weight W of a certain stock of fish is given by W=nw, 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=2t2+3 and w=t2−t+2, then the rate of change of W with respect to t at t=1 is
A
1
B
8
C
13
D
5
Answer
13
Explanation
Solution
Let W=nw ⇒dtdW=ndtdw+w.dtdn...(1) Given : w=t2−t+2 and n=2t2+3 ⇒dtdw=2t−1anddtdn=4t ∴ Equation (1) ⇒dtdw=(2t2+3)(2t−1)+(t2−t+2)(4t) Thus, dtdW∣t=1=(2+3)(2−1)+(2)(4) =5(1)+8=13