Find the maximum value of http://stuff.daniel15.com/cgi-bin/ma...+%2010h%28x%29 given that http://stuff.daniel15.com/cgi-bin/ma...%20%5Cleq%2010.

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- Apr 12th 2009, 10:45 PMusagi_killerMaximum value.
Find the maximum value of http://stuff.daniel15.com/cgi-bin/ma...+%2010h%28x%29 given that http://stuff.daniel15.com/cgi-bin/ma...%20%5Cleq%2010.

- Apr 12th 2009, 11:22 PMCaptainBlack
Without knowing what functions $\displaystyle f,\ g, \ h$ are we cannot say what the actual maximum is but you can establish an upper bound, because clearly:

$\displaystyle a=3f+4g+10h\le100$

when $\displaystyle f,\ g,\ h$ satisfy the constraint $\displaystyle |f+g+h|\le10 $

CB - Apr 13th 2009, 12:57 AMusagi_killer
Sorry!! wrong question lols,

sorry for the inconvenience!!!

The revised question is:

Find the maximum value of $\displaystyle a(x) = 3f(x) + 4g(x) + 10h(x)$ given that $\displaystyle f(x)^2 + g(x)^2 + h(x)^2 \leq 9.$

i've tried putting everything in terms of each other but its not working haha