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Question

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

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Solution

The slope of the x-axis is 0.
Now, let (x1, y1) be the required point.
Here,
Since, the point lies on the curve.Hence, y1=x12-2x1+3 ... 1Now, y=x2-2x+3dydx=2x-2Slope of the tangent at x, y=dydxx1, y1=2x1-2Given:Slope of the tangent at x1, y1=Slope of the x-axis=2x1-2=0x1=1andy1=1-2+3=2 [From (1)]Required point=x1, y1=1, 2

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