Find the point on the curve y = x² – 2x + 3, where the tangent is parallel to x-axis.

Given curve y = x² – 2x + 3

We know that the slope of the x-axis is 0.

Let the required point be (a, b).

∵ the point lies on the given curve

∴ b = a² – 2a + 3 ….(1)

Now, y = x² – 2x + 3

Slope of the tangent at (a, b) = 2a – 2

According to the question,

2a – 2 = 0

⇒ a = 1

Putting this in (1),

b = 1 – 2 +3

⇒ b = 2

So, the required point is (1, 2)