×
Get Full Access to Calculus: Early Transcendental Functions - 6 Edition - Chapter 16.1 - Problem 6
Get Full Access to Calculus: Early Transcendental Functions - 6 Edition - Chapter 16.1 - Problem 6

×

# ?Solving an Exact Differential Equation In Exercises 5-14, determine whether the differential equation is exact. If it is,find the general solution.

ISBN: 9781285774770 141

## Solution for problem 6 Chapter 16.1

Calculus: Early Transcendental Functions | 6th Edition

• Textbook Solutions
• 2901 Step-by-step solutions solved by professors and subject experts
• Get 24/7 help from StudySoup virtual teaching assistants

Calculus: Early Transcendental Functions | 6th Edition

4 5 1 397 Reviews
21
2
Problem 6

Solving an Exact Differential Equation In Exercises 5-14, determine whether the differential equation is exact. If it is,find the general solution.

$$y e^{x} d x+e^{x} d y=0$$

Text Transcription:

y e^x dx+e^x dy=0

Step-by-Step Solution:

Step 1 of 5) Theorem 11—Second Derivative Test for Local Extreme Values Suppose that ƒ(x, y) and its first and second partial derivatives are continuous throughout a disk centered at (a, b) and that ƒx(a, b) = ƒy(a, b) = 0. Then i) ƒ has a local maximum at (a, b) if ƒxx 6 0 and ƒxx ƒyy - ƒxy 2 7 0 at (a, b). ii) ƒ has a local minimum at (a, b) if ƒxx 7 0 and ƒxx ƒyy - ƒxy 2 7 0 at (a, b). iii) ƒ has a saddle point at (a, b) if ƒxx ƒyy - ƒxy 2 6 0 at (a, b). iv) the test is inconclusive at (a, b) if ƒxx ƒyy - ƒxy 2 = 0 at (a, b). In this case, we must find some other way to determine the behavior of ƒ at (a, b).

Step 2 of 2

## Discover and learn what students are asking

Statistics: Informed Decisions Using Data : Tests for Independence and the Homogeneity of Proportions
?The following table contains observed values and expected values in parentheses for two categorical variables, X and Y, where variable X has three cat

Statistics: Informed Decisions Using Data : Testing the Significance of the Least-Squares Regression Model
?Why don’t we conduct inference on the linear correlation coefficient?

Chemistry: The Central Science : Chemical Reactions and Reaction Stoichiometry
?The compound $$\mathrm{XCl}_{4}$$ contains 75.0 % CI by mass. What is the element X?

#### Related chapters

Unlock Textbook Solution