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Question
Find the minimum value of the function f(x) = |x-1| + |x-2| + |x-3| + ... + |x-20|
Find the minimum value of the function f(x) = |x-1| + |x-2| + |x-3| + ... + |x-20|
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Solution
The correct option is D 100
The minimum value of such an expression occurs when x takes the middle value in the given range i.e. when x is between 10 and 11. And the value of the function f(x) at that value becomes:
f(x=10) = 9+8+7+6+5+4+3+2+1+0+1+2+3+4+5+6+7+8+9+10 = 100
Also,f(x=11) = 10+9+8+7+6+5+4+3+2+1+0+1+2+3+4+5+6+7+8+9=100 Therefore, answer option (d) stands out as the correct answer choice.
100
The minimum value of such an expression occurs when x takes the middle value in the given range i.e. when x is between 10 and 11. And the value of the function f(x) at that value becomes:
f(x=10) = 9+8+7+6+5+4+3+2+1+0+1+2+3+4+5+6+7+8+9+10 = 100
Also,f(x=11) = 10+9+8+7+6+5+4+3+2+1+0+1+2+3+4+5+6+7+8+9=100
Therefore, answer option (d) stands out as the correct answer choice.
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