Part 4

Algebra Level 2

y = X 2015 + X 2016 y=\left | X-2015 \right |+\left | X-2016 \right | Find minimum of the function above

1 2015 2 4 5 2016 3 6

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1 solution

Kay Xspre
Jan 6, 2016

y = { 4031 2 x if x 2015 1 if 2015 x 2016 2 x 4031 if x 2016 y = \begin{cases} 4031-2x & \text{ if } x\leq 2015 \\ 1 & \text{ if } 2015 \leq x \leq 2016 \\ 2x-4031 & \text{ if } x\geq 2016 \end{cases} When we split cases, we can determine the minimum value to be 1 over all cases, hence m i n ( y ) = 1 min(y) = 1

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