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Question

For the function f(x)=4x24x+2+|x| , which of the following holds good 
  1. The least value of the function is 3+122
     
  2. The least possible value of function is 3+12 
  3. The function takes its least value at x=336  
  4. Function has exactly one point of minima


Solution

The correct options are
C The function takes its least value at x=336  
D Function has exactly one point of minima
y=4x24x+2+|x|
    =(2x1)2+1+|x|
if x<0
y=(2x1)2+1x
y=(2x1)2(2x1)2+11y<0   x<0
if x>0
y=(2x1)2+1+x
y=2(2x1)(2x1)2+1+1
y>0 3123<x<
y<00<x<3123


minima at x=3123 

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