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question mark

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

Aditya Kartikeya , 10 Years ago
Grade 10
anser 1 Answers
Y RAJYALAKSHMI

Last Activity: 10 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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