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If `m and M` respectively denote 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

A

(-3,19)

B

(3,19)

C

(-19 , 3)

D

(-19 ,-3)

Text Solution

Verified by Experts

The correct Answer is:
B
We have `f(x)=x(x-1)^2+3`
`rArr f(x)=2 (x-1) lt 0 " for all " x in [ -3,1]`
So f(x) is decreasing [-3 , 1]
`rArr m=f(1)` and M = f (-3) `rArr` m=3 and M=19 (m,M)=(3,19 )
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