Question

Find all the points (x,y) where f(x,y) has a possible relative maximum or minimum:

f(x,y)=x^4-8xy+2y^2-3

Answer 1

I found the derivative for x and y. After that I set them equal to 0 to find the two expressions for y. I then equated the two expressions of y. I am just now having a hard time solving for what x is. If someone can help me, I would greatly appreciate it

Answer 2

Are you able to show us the equation that you're solving for \(x\)? It might be easier.

Answer 3

yeah, sure. I hope it's correct: 4x^3/8=8x/4

Answer 4

Yes, it is. Now just solve for x

Answer 5

That's what I am having difficulties with. I guess I just don't know how to get the x by itself. The x^3 is throwing me off

Answer 6

Hint: common factor : x

Answer 7

This is from Calc III?

Answer 8

No, Calc I...lol. I am not that advanced in calculus

Answer 9

Since when is Calc I multivariable?

Answer 10

Are you covering implicit differentiation atm?

Answer 11

lol. I am covering maxima and minima of functions of several variables

Answer 12

Functions of several variables are covered in Multivariable Calculus which is part of Calc III. Calc I is supposed to be single-variable...

Answer 13

@drawar would it be 16x^2(x-4)=0. I am a little lost

Answer 14

@genius12 not the one I am taking

Answer 15

what is your course textbook?

Answer 16

No, simplify the expression, this may help: 4x^3/8=8x/4 can be simplified into x^3=4x, which is equivalent to x^3-4x=0. Now take out the common factor x and ...

Answer 17

@drawar is x=2?

Answer 18

is x=2?

Answer 19

http://www.wolframalpha.com/input/?i=relative+extrema+of+f%28x%2Cy%29%3Dx^4-8xy%2B2y^2-3

@aebiri2

Answer 20

x=-2 and x=0 as well

Answer 21

@genius12 I am all types of confused...lol. How did you come up with this?

Answer 22

@drawar can you please please work it out for me. I can see how x=0, but -2????

Answer 23

x^3-4x=x(x^2-4)=x(x-2)(x+2), just a matter of factorization...

Answer 24

@drawar oh, ok. gotcha. so x=0, x=2, x=-2

Answer 25

Yes, plug them back into the partial derivatives to find y's. Then calculate the value of f for each (x,y) and compare them.

Answer 26

ok, thank you so so much. I really appreciate it!

Answer 27

nps :)