Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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**Use Partial Derivatives to Locate Critical Points for a Function of Two Variables**

**Problem Statement:**

Find the values of \( x, y, \) and \( z \) that correspond to the critical point of the function:

\[ z = f(x, y) = 3x^2 + 8x - 7y + 5y^2 + 7xy \]

Enter your answer as a decimal number, or a calculation (like 22/7).

**Answer Fields:**

- \( x = \)  [Input field]  (Round to 4 decimal places)

- \( y = \)  [Input field]  (Round to 4 decimal places)

- \( z = \)  [Input field]  (Round to 4 decimal places)

**Additional Resources:**

- Question Help: [Video link]

**Submission:**

- [Submit Question Button]
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Transcribed Image Text:**Use Partial Derivatives to Locate Critical Points for a Function of Two Variables** **Problem Statement:** Find the values of \( x, y, \) and \( z \) that correspond to the critical point of the function: \[ z = f(x, y) = 3x^2 + 8x - 7y + 5y^2 + 7xy \] Enter your answer as a decimal number, or a calculation (like 22/7). **Answer Fields:** - \( x = \) [Input field] (Round to 4 decimal places) - \( y = \) [Input field] (Round to 4 decimal places) - \( z = \) [Input field] (Round to 4 decimal places) **Additional Resources:** - Question Help: [Video link] **Submission:** - [Submit Question Button]
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