BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 4, Problem 7P
To determine

The highest and lowest value of the curve of the equation.

Expert Solution

Explanation of Solution

Given information:

The equation is,

  x2+xy+y2=12

Calculations:

Here the equation is,

  x2+xy+y2=12

Now the highest and lowest value of the equation can be determined by differentiating the equation,

Differentiating the equation,

  x2+xy+y2=122x+xdydx+y+2ydydx=0Now, for getting maximum and minimum,dydx=0.Therefore,2x+xdydx+y+2ydydx=02x+y=0y=2x

Now, substituting the value of y in the above equation,

  x2+xy+y2=12               Putting y=2x x 2 +x(2x)+ (2x) 2 =12x22x2+4x2=123x2=12x2=4x=±2

Again putting the value of x=±2 in the above equation, we get,

  y=±4

Now considering all the values of x and y and putting them in the equation, we get the highest point is x=2 and y=4 .

The lowest point of the curve is x=2 and y=4 .

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