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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 ∴ $(m, M)=(3,19)$. |
