# Lagrange multiplier method

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
Staff Emeritus
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
Homework Helper
Uh, substitute (1,0) into f?

i get (0,0)?

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

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
Homework Helper
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!

'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