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Question

lf m and M respectively denote the minimum and mximum of f(x)=(x1)2+3 for x[3,1] then the ordered pair (m, M) =

A
(3,19)
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B
(3,19)
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C
(19,3)
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D
(19,3)
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Solution

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

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