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Hello again,
I have another level curves related question, which I tried solving, but I have the feeling that I did something wrong, would appreciate it if you could have a look.
The question is:
The function f is given by:
\[f(x,y)=x^{2}+\sqrt{x+2y}\]
C1 is the level curve that goes through (1,4). C2 is the level curve that goes through (2,1) and C3 is the level curve that goes through (3,4).
For each statement, decide true or false:
a. C1=C3
b. C1=C2
c. C1 and C3 do not intersect
d. C2=C3
e. C1 and C2 has exactly two points of intersection
The attached photos show my attempt.
My conclusion is:
a. false
b. true
c. false
d. false
e. false (they are the same, so having more than 2?)
thank you !
I have another level curves related question, which I tried solving, but I have the feeling that I did something wrong, would appreciate it if you could have a look.
The question is:
The function f is given by:
\[f(x,y)=x^{2}+\sqrt{x+2y}\]
C1 is the level curve that goes through (1,4). C2 is the level curve that goes through (2,1) and C3 is the level curve that goes through (3,4).
For each statement, decide true or false:
a. C1=C3
b. C1=C2
c. C1 and C3 do not intersect
d. C2=C3
e. C1 and C2 has exactly two points of intersection
The attached photos show my attempt.
My conclusion is:
a. false
b. true
c. false
d. false
e. false (they are the same, so having more than 2?)
thank you !
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