Let's say we have some polynomial of degree 2: $P(x) = 2x^2 - 7x + 6$. How can I find polynomial $Q(x)$ of degree at most 1 such that maximum value of $|P(x) - Q(x)|$ in range $x\in[0,1]$ is minimum.
Is there any trick for this kind of problems?
I have tried to set $Q(x) = ax + b$, then I can see that $b$ just shifts the range of $P(x) - Q(x)$. Since values of $x$ are positive, it kind of make sense to set $a=7$, but I am not sure.