Question

Find the minimum value of |x-2|+|x+2|​

Answer 1

When X = 1

|X| = 1

|X-1| = 0

|X-2| = 1

|X-3| = 2

Now,

|X| + |X-1| + |X-2| + |X-3| = 1 + 0 + 1 +2 = 4

Similarly , When X = 2

|X| = 2

|X-1| = 1

|X-2| = 0

|X-3| = 1

Now,

|X| + |X-1| + |X-2| + |X-3| = 2 + 1 + 0 + 1 = 4

When X = 0

|X| = 0

|X-1| = 1

|X-2| = 2

|X-3| = 3

Now,

|X| + |X-1| + |X-2| + |X-3| = 0 + 1 + 2 + 3 = 6

When X = 3

|X| = 3

|X-1| = 2

|X-2| = 1

|X-3| = 0

Now,

|X| + |X-1| + |X-2| + |X-3| = 3 + 2 + 1 + 0 = 6

Hence the minimum value is 4 at x = 1 and at x = 2

Maximum value is 6 at x = 0 and at x = 3

Hope it helps you dear