If m and M respectively the minimum and maximum of $f(x)=(x-1)^2+3$ for $x \in[-3,1]$, then the ordered pair (m, M) is equal to

$(-3,19)$ $(3,19)$ $(-19,3)$ $(-19,-3)$

$(3,19)$

We have, $f(x)=(x-1)^2+3$ $\Rightarrow f'(x)=2(x-1)<0$ for all $x \in[-3,1]$ So, f(x) is decreasing $[-3,1]$ $\Rightarrow m=f(1)$ and $M=f(-3) \Rightarrow$ m = 3 and M = 19 ∴  $(m, M)=(3,19)$.