   Chapter 11.3, Problem 54E ### 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

# In Problems 53 and 54, find the maximum and mini- mum values of y. Use a graphing utility to verify your conclusion. 4 x 2 + y 2 − 8 x = 0

To determine

To calculate: The maximum and minimum values of y if 4x2+y28x=0.

Explanation

Given Information:

The provided equation is:

4x2+y28x=0

Formula used:

The power rule of derivative,

ddxxn=nxn1

Calculation:

Consider the provided equation:

4x2+y28x=0

Differentiate the both sides of the equation with respect to x as:

ddx(4x2+y28x)=ddx(0)

Now, apply the power rule of derivative:

ddx(4x2+y28x)=ddx(0)8x+2yy8=0

Solve for y as:

8x+2yy=8yy=44xy=44xy

Now, the curve attains its maxima or minima where its derivative is zero

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