Question

lf m and M respectively denote the minimum and mximum of $f\left(x\right)=(x-1{)}^2+3$ for $x\in [-3,1]$ then the ordered pair (m, M) =

• A. $(-3,19)$
• B. $(3,19)$
• C. $(-19,3)$
• D. $(-19,-3)$

Answer 1

Answer: (B)

$(3,19)$

$f\left(x\right)$ is the sum of a square and a constant term. It will acquire minimum value when the square term becomes zero.
Hence,
$f\left(x\right)$ is min at $x=1$
$f\left(1\right)=3$
The other extreme value will occur at the other end point.
$f\left(x\right)$ is max at $x=-3$
$f(-3)=19$