   Chapter 8.4, Problem 8CP ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Using the model from Example 8, find the rate at which sales are changing when t =   59 .

To determine

To calculate: The rate at which sales are changing at t=59, when sales of manufacturing fertilizer is modeled as F=100000[1+sin2π(t60)365].

Explanation

Given Information:

The sales of manufacturing fertilizer is modeled as F=100000[1+sin2π(t60)365].

Formula used:

Sine derivative Rule:

ddx[sinu]=cosududx

General power derivative rule:

ddxxn=nxn1

Reduction formula for trigonometric identity.

cos(θ)=cosθ

Calculation:

Consider the provided trigonometric function:

F=100000[1+sin2π(t60)365]

Differentiate the above function with respect to t using Sine and Power derivative rules.

dFdt=ddt{100000[1+sin2π(t60)365]}=100000ddt[1+sin2π(t60)365]=100000[0+cos2π(t60)365

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