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suppose x1, and x2 are the point of maxi...

suppose `x_1,` and `x_2` are the point of maximum and the point of minimum respectively of the function `f(x)=2x^3-9ax^2 + 12a^2x + 1` respectively, `(a> o)` then for the equality `x_1^2 = x_2` to be true the value of `'a'` must be

A

0

B

2

C

1

D

`(1)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
B
`6(x^(2) -3ax +2a^(2))`
`= 6 (x-a) (x-2a), a gt 0`
`x=a` is point of maxima
`x=2a ` is point of minima
`:.a^(2)=2a`
`rArr a=0 or a = 2`
but `a gt 0 rArr a =2`
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