+-
- -MlT2 li15~+-
ASSIGNMEN~ 3 +-
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DUE: JUILY 2026
DISCLAIMER:
- THIS-OttlJMENTTSrDnEFERENCE AND71UI lNCE PUR ES-
DNLY. I DD NDTt TAKE RESPµNSIBIUITY !FDR AN~ PLAGIARl~M. tMISUS . DR
ACADEMIC MISCONDUCT RESULTING FROM THSIR USE. IT IS YOUR ~
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RELEVANT GUlr LINES DR STANDARDr l1
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1
, PLEASE USE THIS DOCUMENT AS A GUIDE TO ANSWER YOUR ASSIGNMENT
Question 1
(a) Find all critical points
Critical points occur where the gradient "ii f = 0, meaning both first-order partial
derivatives must equal zero simultaneously.
1. Calculate the partial derivatives:
• f z = fz(x 2 - 6x - 3y2 - y 3 ) = 2:i: - B
• / y = ~(x 2 - 6x .L 3y2 - y 3 ) = By - 3y2
2. Set them to zero and solve:
• 2:t-B= 0 =} X= 3
• By - 3y2 = 0 => 3y(2 - y) = 0 => y = 0 or y = 2
Critica l Points: Combining these results, we find the two critical points:
1. (3,0)
2. (3. 2)
- -MlT2 li15~+-
ASSIGNMEN~ 3 +-
t t f t
lttt oues711!1Nfs Fm1:f1:.v AN. WERED
1
DUE: JUILY 2026
DISCLAIMER:
- THIS-OttlJMENTTSrDnEFERENCE AND71UI lNCE PUR ES-
DNLY. I DD NDTt TAKE RESPµNSIBIUITY !FDR AN~ PLAGIARl~M. tMISUS . DR
ACADEMIC MISCONDUCT RESULTING FROM THSIR USE. IT IS YOUR ~
T
RESPDNSIBILITt T ENSU E ORIGINALITY AN~ CDMPLIAN E WITH
RELEVANT GUlr LINES DR STANDARDr l1
~ T
1
, PLEASE USE THIS DOCUMENT AS A GUIDE TO ANSWER YOUR ASSIGNMENT
Question 1
(a) Find all critical points
Critical points occur where the gradient "ii f = 0, meaning both first-order partial
derivatives must equal zero simultaneously.
1. Calculate the partial derivatives:
• f z = fz(x 2 - 6x - 3y2 - y 3 ) = 2:i: - B
• / y = ~(x 2 - 6x .L 3y2 - y 3 ) = By - 3y2
2. Set them to zero and solve:
• 2:t-B= 0 =} X= 3
• By - 3y2 = 0 => 3y(2 - y) = 0 => y = 0 or y = 2
Critica l Points: Combining these results, we find the two critical points:
1. (3,0)
2. (3. 2)
