What Is the Minimum Value of y in the Given Expression?

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SUMMARY

The minimum value of the expression y = |x| + |x-1| + |x-3| + |x-6| + ... + |x-5151| occurs at two adjacent integer points. The total number of terms in the expression, denoted as m, is 5152. The number of integers for which y achieves its minimum value, denoted as n, is also relevant for calculating the expression (m+n-18)/10. The slope of the function is -5152 for negative x and increases by 2 at each integer transition.

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If y = \mid x \mid+\mid x-1 \mid+\mid x-3 \mid+\mid x-6 \mid+...+\mid x-5151 \midand m = no. of terms in the expression yand n = no. of integers for which y has min. valueThen \displaystyle\frac{m+n-18}{10} =
 
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jacks said:
If y = \mid x \mid+\mid x-1 \mid+\mid x-3 \mid+\mid x-6 \mid+...+\mid x-5151 \midand m = no. of terms in the expression yand n = no. of integers for which y has min. valueThen \displaystyle\frac{m+n-18}{10} =

Maybe it's me, but I find that incomprehensible.

For a start why is \(m\) not \(5152\)?

Do you mean \(n\) to be the number of integers corresponding to a local minima of \(y\)? You can show that there is a global minimum and it achived this at two adjacent integer points.

(the slope is -5152 for -ve \(x\), and increases by 2 when we pass a integer argument moving to the right ...)

CB
 
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