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Question

Let f(x)=5|x2| and g(x)=|x+1|,xR. If f(x) attains maximum value at α and g(x) attains minimum value at β, then limxαβ(x1)(x25x+6)x26x+8 is equal to:
  1. 12
  2. 32
  3. 12
  4. 32


Solution

The correct option is C 12
f(x)=5|x2|
f(x) attains maximum value when  
|x2|=0x=2=αg(x)=|x+1|
g(x) attains minimum value when x=1=β
limxαβ(x1)(x25x+6)x26x+8=limx2(x1)(x2)(x3)(x2)(x4)=12

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