# Thread: Maximum and minimum values

1. ## Maximum and minimum values

find the max and min values of the function f(x,y,z,t)= (x+y+z+t) subject to the constraint $x^2+y^2+z^2+t^2=49$
I have never calculated for t before and I'm thrown off as how to do it.
You get no critical points from the original equation so I'm assuming it would all be on the boundary. Please help
thank you

2. Originally Posted by koalamath
find the max and min values of the function f(x,y,z,t)= (x+y+z+t) subject to the constraint $x^2+y^2+z^2+t^2=49$
I have never calculated for t before and I'm thrown off as how to do it.
You get no critical points from the original equation so I'm assuming it would all be on the boundary. Please help
thank you
Have you learned the method of Lagrange multipliers? The fact that t is in it just means you have 4 variables to solve for.

3. no i havent'

4. ## Thank you mr fantastic

ok so i found lambda to be $+or- 1/7$ There fore x,y,z,t would $+or-7/2$
This leads to a max of 14 at $(2/7,2/7,2/7,2/7)$ and a min at $(-2/7,-2/7,-2/7,-2/7)$
correct?