Max return a partial false result

savecancel

Suppose I have four (may be more) linear functions say :

f0(x) = -3 x
f1(x) = -3 x + 1
f2(x) = -6 x + 2
f3(x) = -9 x + 3

for $x \in [0, 1]$. They are easy to plot

plot((f0(x),f1(x),f2(x),f3(x)),(x,0,1),color=['red','blue','green','cyan'])

So one can see that for $x \in [0,1/3[$ $\max{f0(x),f1(x),f2(x),f3(x)} = f3(x)$ and for $x \in ]1/3, 1]$, $\max{f0(x),f1(x),f2(x),f3(x)} = f1(x)$.

But

max(f0(x),f1(x),f2(x),f3(x))

return only $f1(x)$. How to correct this result ?