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Problem 51 Medium Difficulty

Biologists have proposed a cubic polynomial to model the length $ L $ of Alaskan rockfish at age $ A: $
$ L = 0.0155A^3 - 0.372A^2 + 3.95A + 1.21 $
where $ L $ is measured in inches and $ A $ in years. Calculate
$ \frac{dL}{dA}\mid A=12 $

Answer

$$\left.\frac{d L}{d A}\right|_{A=12}=0.0465(12)^{2}-0.744(12)+3.95=1.718$$

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Video Transcript

he is. Claire's the one you're in here. So we have a s the variable, and we have a deal over t A. Since Alice people to hell of a D over D A. And we have our equation would just 0.155 You're cute. Minus 0.372 C square plus 3.95 a less 1.21 Is this equal? 2.4658 square minus 0.744 a plus 3.95 We're gonna plug in a is equal to 12 and we get 1.7 on the interest per year. And the derivative is interpreted as our instantaneous rate of growth off the fish. Uh, aged well.