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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 $

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00:57

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 1

Derivatives of Polynomials and Exponential Functions

Derivatives

Differentiation

Oregon State University

Harvey Mudd College

Baylor University

Lectures

04:40

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

44:57

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

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Biologists have proposed a…

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Fish growth Biologists hav…

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Halibut growth The length …

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Fish length Assume the len…

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A 1999 study by Starkey an…

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.

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