   Chapter 11.3, Problem 56E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Insect control Suppose that the number of mosquitoes N (in thousands) in a certain swampy area near a community is related to the number of pounds of insecticide x sprayed on the nesting areas according to N x − 10 x + N = 300 Find the rate of change of N with respect to x when 49 pounds of insecticide is used.

To determine

To calculate: The rate of change of N with respect to x when 49 pounds of insecticide is used if the relation is Nx10x+N=300.

Explanation

Given Information:

Number of mosquitos N (in thousands) in a certain swampy area is related to the number of pounds of insecticide x sprayed on the nesting areas according to the equation, Nx10x+N=300.

Formula used:

According to the product rule of derivatives,

ddx(uv)=udvdx+vdudx

Calculation:

The number of mosquitos N in a certain swampy area is related to the number of pounds of insecticide x sprayed on the nesting areas is,

Nx10x+N=300

Now, the rate of change of N with respect to x is given by dNdx.

Now, differentiate both sides with respect to x as,

ddx(Nx10x+N)=ddx(300)

Now, use the product rule of derivatives,

To obtain the derivative of Nx as:

ddx(Nx)ddx(10x)+dNdx=0

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