Maximum value.

**usagi_killer** · April 12th 2009, 10:45 PM

Find the maximum value of $a(x) = 3f(x) + 4g(x) + 10h(x)$ given that $\left| f(x) + g(x) + h(x) \right| \leq 10$ .

**CaptainBlack** · April 12th 2009, 11:22 PM

Originally Posted by usagi_killer

Find the maximum value of $a(x) = 3f(x) + 4g(x) + 10h(x)$ given that $\left| f(x) + g(x) + h(x) \right| \leq 10$ .

Without knowing what functions $f,\ g, \ h$ are we cannot say what the actual maximum is but you can establish an upper bound, because clearly:

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

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

CB

**usagi_killer** · April 13th 2009, 12:57 AM

Sorry!! wrong question lols,
sorry for the inconvenience!!!

The revised question is:

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

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

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