Maxima and MinimaMedium
Question
The least value of 2(x2-3)3 + 27 is-
Options
A.227
B.2
C.1
D.None of these
Solution
2(x2 - 3)3 + 27 is minimum when
(x2 - 3)3 + 27 is minimum
Since (x2 - 3)3 + 27 = x6 - 9x4 + 27 x2
= x2(x4 - 9x2 + 27)
= x2[x2 - 9/2)2 + 27/4]
≥ 0 for all x.
∴ minimum value of (x2 - 3)2 27 = 0
Thus, minimum value of 2(x2-3)3 + 27 is 2o = 1
(x2 - 3)3 + 27 is minimum
Since (x2 - 3)3 + 27 = x6 - 9x4 + 27 x2
= x2(x4 - 9x2 + 27)
= x2[x2 - 9/2)2 + 27/4]
≥ 0 for all x.
∴ minimum value of (x2 - 3)2 27 = 0
Thus, minimum value of 2(x2-3)3 + 27 is 2o = 1
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