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

### Single Variable Calculus: Concepts...

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

### 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 .

### Have a homework question?

Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!