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Question

The minimum value of the expression y=|x2|+|x+4|+|x6| is
  1. 8
  2. 10
  3. 14
  4. 6


Solution

The correct option is B 10
y=|x2|+|x+4|+|x6|
Here the turning points are 4,2,6

|x2|+|x+4|+|x6|=⎪ ⎪ ⎪⎪ ⎪ ⎪(x2)(x+4)(x6),x<4(x2)+(x+4)(x6),4x<2(x2)+(x+4)(x6),2x<6(x2)+(x+4)+(x6),x6

|x2|+|x+4|+|x6|=⎪ ⎪⎪ ⎪43x,x<412x,4x<28+x,2x<63x4,x6


Hence, the minimum value of the expression is 10.

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