Find the maximum value of given that .
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
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