Maximizing f(x,y) on y=1-x^2 using Lagrange Multiplier Method

[sara_87]

Question:

Use Lagrange multiplier method to determine the point on the curve
y=1-x^2
that maximises the function f(x,y)=2x + y.
Hence find the maximum value of f.

Attempt at Solution:

Okay I used the Lagrange method to get a point on the curve and I got (1,0)

How do I find the maximum value of f though?

 

[cristo]

If you've found the values of x and y where the function has a maximum, then do you not just plug (1,0) into f(x,y) to obtain the value of the function at that point?

 

[Dick]

Uh, substitute (1,0) into f?

 

[sara_87]

i get (0,0)?

 

[Dick]

f is a number. Not a point. And it's not 0.

 

[sara_87]

i'm still stuck! i don't what to do lol
give me more tips before i give up on maths altogether!
(does anyone else go through a phase when they just want to give up? lol)

 

[Dick]

You say f(x,y)=2*x+y. You've found a solution (1,0) so x=1, y=0. What is f(x,y)? Don't get so flustered!

 

[sara_87]

'Don't get so flustered!'

you don't know what kind of day I've had! lol

thank you for your help and time I'm sure it's not a hard question i'll think about it tomorrow when i feel more awake.

 

[Dick]

Your annoyance is blocking you from seeing the obvious. That makes it a really good time to take a rest.