   Chapter 3.1, Problem 51E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Biologists have proposed a cubic polynomial to model the length L of Alaskan rockfish at age A:L = 0.0 155A3 – 0.372A2 + 3.95A + 1.21where L is measured in inches and A in years. Calculate d L d A | A = 12 and interpret your answer.

To determine

To calculate: The rate of change of the length of Alaskan rockfish at age 12.

Explanation

Given:

The length (L) of Alaskan rockfish at age A is L=0.0155A30.372A2+3.95A+1.21 where L is measured in inches and A in years.

Derivative rules:

(1) Derivative of Constant Function: ddt(c)=0

(2) Constant Multiple Rule: ddx[cf(x)]=cddxf(x)

(3) Power Rule: ddx(xn)=nxn1

(4) Difference Rule: ddx[f(x)g(x)]=ddx(f(x))ddx(g(x))

(5) Sum Rule: ddx[f(x)+g(x)]=ddx(f(x))+ddx(g(x))

Calculation:

Obtain the first derivative of L with respect to A.

dLdA=ddA(0.0155A30.372A2+3.95A+1.21)

Apply the derivative rules (4) and (5) to get,

dLdA=ddA(0.0155A3)ddA(0.372A2)+ddA(3.95A)+ddA(1.21)

Apply the derivative rules (1) and (2) to get

dLdA=ddA(0

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Find more solutions based on key concepts 