Find all local maxima, local minima, and saddle points of each function. Enter each point as an ordered triple, e.g., "(1,5,10)". If there is more than one point of a given type, enter a comma- separated list of ordered triples. If there are no points of a given type, enter "none". f(x,y)= e²y8yez Local maxima are none ⠀⠀⠀ Local minima are none Saddle points are none ⠀⠀
Find all local maxima, local minima, and saddle points of each function. Enter each point as an ordered triple, e.g., "(1,5,10)". If there is more than one point of a given type, enter a comma- separated list of ordered triples. If there are no points of a given type, enter "none". f(x,y)= e²y8yez 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
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:# Finding Local Maxima, Minima, and Saddle Points
In this activity, you are asked to find all local maxima, local minima, and saddle points of the given functions. Enter each point as an ordered triple, e.g., "(1, 5, 10)." If there is more than one point of a given type, enter a comma-separated list of ordered triples. If there are no points of a given type, enter "none".
## Function 1: \( f(x, y) = e^{2y} - 8ye^{6x} \)
1. **Local Maxima**:
- Points: none
2. **Local Minima**:
- Points: none
3. **Saddle Points**:
- Points: none
## Function 2: \( f(x, y) = e^x (3x^2 - 7y^2) \)
1. **Local Maxima**:
- Points: none
2. **Local Minima**:
- Points: none
3. **Saddle Points**:
- Points: none
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