calculus-2-asg-3: Consider thefunction Assignment 3 𝑓(𝑥, 𝑦) = 𝑥 3 − 3𝑥 2 + 𝑥𝑦 − 𝑦 3 + 𝑥 + 𝑦 in the square 𝑆given by 0 ≤ 𝑥 ≤ 2,0 ≤ 𝑦 ≤ 2 1. Find the critical point of 𝑓in 𝑆. 2. Knowing the location of the critical points,what can you say about the points in 𝑆where 𝑓 attains its maximum and minimum? 3. Find the maximum and the minimum of 𝑓 in 𝑆and the points at which these values are achieved. 4. Classify the criticalpoints according tothe secondderivative test andsketch the level curves near each such point. 5. What additional information beyond what you found in part (1) does the type of the critical points tell you concerning the location of the maximum and the minimum? If you had carried out the classification of the critical pointion part (4) before part (3), what computation(s) would you have been spared

 𝑓(𝑥, 𝑦) = 𝑥 3 − 3𝑥 2 + 𝑥𝑦 − 𝑦 3 + 𝑥 + 𝑦 in the square 𝑆given by 0 ≤ 𝑥 ≤ 2,0 ≤ 𝑦 ≤ 2 

1. Find the critical point of 𝑓in 𝑆. 

2. Knowing the location of the critical points,what can you say about the points in 𝑆where 𝑓 attains its maximum and minimum? 

3. Find the maximum and the minimum of 𝑓 in 𝑆and the points at which these values are achieved.

 4. Classify the critical points according to the second derivative test and sketch the level curves near each such point. 

5. What additional information beyond what you found in part (1) does the type of the critical points tell you concerning the location of the maximum and the minimum? If you had carried out the classification of the critical points in part (4) before part (3), what computation(s) would you have been spared