# Maximum and minimum values

• Nov 19th 2008, 03:00 AM
koalamath
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 \$\displaystyle 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
• Nov 19th 2008, 03:07 AM
mr fantastic
Quote:

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 \$\displaystyle 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.
• Nov 19th 2008, 04:08 AM
koalamath
no i havent'
• Nov 19th 2008, 11:29 AM
koalamath
Thank you mr fantastic
ok so i found lambda to be \$\displaystyle +or- 1/7\$ There fore x,y,z,t would \$\displaystyle +or-7/2\$
This leads to a max of 14 at \$\displaystyle (2/7,2/7,2/7,2/7)\$ and a min at \$\displaystyle (-2/7,-2/7,-2/7,-2/7)\$
correct?