f(x, y) = ln(108x +9y) + 6x² - 9y Local maxima are none Local minima are none Saddle points are none #

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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## Function Analysis of \( f(x, y) \)

### Given Function:
\[ f(x, y) = \ln(108x + 9y) + 6x^2 - 9y \]

### Critical Points Analysis:
The function \( f(x, y) \) does not have any local maxima, local minima, or saddle points.

- **Local maxima are**: none
- **Local minima are**: none
- **Saddle points are**: none

This analysis indicates that the function does not achieve any local maxima, minima, or saddle points within the specified domain.
Transcribed Image Text:## Function Analysis of \( f(x, y) \) ### Given Function: \[ f(x, y) = \ln(108x + 9y) + 6x^2 - 9y \] ### Critical Points Analysis: The function \( f(x, y) \) does not have any local maxima, local minima, or saddle points. - **Local maxima are**: none - **Local minima are**: none - **Saddle points are**: none This analysis indicates that the function does not achieve any local maxima, minima, or saddle points within the specified domain.
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