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
Answer & explanation
Correct answer: option 2
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
∴ $(m, M)=(3,19)$.