Extrema of functions of Two Variables

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CalleighMay

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Hello, my name is Calleigh and i am new to the forum! I am in Calculus II and have a few questions on some problems. I am using the textbook Calculus 8th edition by Larson, Hostetler and Edwards. Could someone please help me?

The problem is on pg 959 in chapter 13.8 in the text, number 56. It reads:

a. Find the absolute extrema of the function.
b. From the form of he function, determine whether a relative maximum of a relative minimum occurs at each point.

and it gives:
f(x,y)=2x-2xy+y^2
and R:The region in the xy-plane bounded by the graphs of y=x^2 and y=1


What does it mean when it states f(x,y)??? I've already heard of f(x). I don't know what it means when it has both x and y in the parenthesis. My professor gave these problems to us even though we haven't covered it yet, but he expects us to know how to do it?? Please help me, i'm so lost...


Any help would be greatly appreciated! Thanks guyssss ;)
 
How did you gert this far having NEVER encountered a function of more than one variable?

f(x,y,z,w,r,t) indicates a function of the variables listed it the parentheses.

a. Why would this function of x and y have absolute extrema? A quick glance suggests it is unbounded in every cardinal direction.
 
I checked for any typo's when copying the problem here and it's what the book states, could someone please help me solve this one? =/
 
CalleighMay said:
I checked for any typo's when copying the problem here and it's what the book states
Click to expand...
The tutor wasn't questioning the validity of the "f(x,y)" notation. The tutor was questioning a student's being in this class without ever having even heard of this.

The problem, of course, is that your utter lack of familiarity indicates that you have somehow been placed into a course that skipped at least one prerequisite course. You are missing crucial information that you are "expected" (assumed by the course material) to know.

Unfortunately, we are unable to provide the missing months of classroom instruction. Please have a serious talk with your academic advisor! :shock:

Eliz.
 
AS i stated before in my original post we haven't covered this, our professor has decided to give us a little "preview" of what we're going to see next semester. This stuff hasn't been taught to us yet, we were just supposed to try to figure it out together. I really want to impress him that's why i came to you guys for some help... Thanks for letting me know i am not good enough for you...
 
\(\displaystyle f(x,y)=2x-2xy+y^{2}\)

Derivative wrt x: \(\displaystyle f_{x}=6x=0, \;\ x=0\)

Derivative wrt y: \(\displaystyle f_{y}=4y-4=0 \;\ y=1\)

Then \(\displaystyle f(0,1)=-2\)

On the line \(\displaystyle y=4, \;\ -2\leq x \leq 2\)

So, \(\displaystyle f(x,y)=f(x)=3x^{2}+32-16=3x^{2}-16\)

and the max is 28, the min is 16.

On the curve \(\displaystyle y=x^{2}, \;\ -2\leq x \leq 2\)

\(\displaystyle f(x,y)=f(x)=3x^{2}+2(x^{2})^{2}-4x^{2}=2x^{4}-x^{2}=x^{2}(2x^{2}-1)\)

and the max is at 28 and the min at \(\displaystyle \frac{-1}{8}\).

\(\displaystyle \text{Absolute max:} \;\ 28 \;\ at \;\ (\pm 2, \;\ 4)\)

\(\displaystyle \text{Absolute min:} \;\ -2 \;\ at \;\ (0,1)\)
 
so that's the answer? =D

When you say the max and min, you found those values by finding x when the first deriv is 0, corect? Did you need to use the second deriv as well?

Thanks! =D
 
Dr. Glockman - WRT = "With Respect To". It is an increasingly standard abbreviation. I don't use it, personally.

KallieghMay - You have provided an excellent reason why pictures should not be allowed in signatures on this site. What's the best way to encourage not to do that any more?
 
Well im talking to a lot of my friends who have tried this one and they're saying that this answer is wrong =/

They're sayinf there's a saddle point at (1,1,1) so there isn't a max or min- i dont know what this means lol Any idea if the answer above is correct?
 
tkhunny said:
KallieghMay - You have provided an excellent reason why pictures should not be allowed in signatures on this site. What's the best way to encourage not to do that any more?
Click to expand...
Pictures of nearly-nekkid blonde removed.
 
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