Maxima and MinimaHard
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
Create a free account to view solution
View Solution FreeMore Maxima and Minima Questions
If for a function f(x), f′(b) = 0, f″(b) = 0, f″′(b) > 0, then x = b is-...The first and second order derivatives of a function ƒ(x) exist at all points in (a,b) with ƒ′(c) = 0, w...The point on the curve x2 = 2y which is nearest to (0, 5) is-...The maximum value of sin3 x + cos3 x is -...If f (x) = 4x3 - x2 - 2x +1 and g(x) = then has the value equal to :...