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Suppose x 1 & x 2 are the point of maximum and the point of minimum respectively of the function f(x) = 2x 3 – 9ax 2 + 12a 2 x + 1 respectively, then for the equally x 2 1 = x 2 to be true the value of ‘a’ must be options 0 2 1 1/4

Suppose x1 & x2 are the point of maximum and the point of minimum respectively of the function f(x) = 2x3 – 9ax2 + 12a2x + 1 respectively, then for the equally x21 = x2 to be true the value of ‘a’ must be
 
options
  1.  0
  2. 2
  3. 1
  4. 1/4

Grade:10

1 Answers

Y RAJYALAKSHMI
45 Points
6 years ago
The extreme points are attained at f ’(x) = 0
=> 6x2 – 18ax + 12a2 = 0  
=> x = 2a, a
f ’’(x) = 12x – 18a
f ’’(x) 0 if x = 2a
Hence the min at x = 2a = x1 & max at x = a = x2 
The condition that x12 = x2  => (2a)2 = a  
=> 4a2 – a = 0
=> a = 0 or a = 1/4
 
Ans: 0, 1/4
 
 

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