Y = |x+1| +3 * |x-2|

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вопрос

To find the minimum value of Y, we need to determine the critical points where the absolute values switch signs.

For x ≤ -1:
Y = -(x+1) + 3(x-2) = 2x - 7

For -1 < x ≤ 2:
Y = x+1 + 3(x-2) = 4x - 5

For x > 2:
Y = x+1 + 3(x-2) = 4x - 5

To find the minimum value, we need to find the intersection points of the equations above.

For x = -1, Y = 2(-1) - 7 = -9
For x = 2, Y = 4(2) - 5 = 3

Thus, the minimum value of Y is -9.