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Question

Find the equations of all lines having slope 0 which are tangent to the curve y=1x22x+3.

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Solution

The equation of the given curve is y=1x22x+3.
The slope of the tangent to the given curve at any point (x,y) is given by,
dydx=(2x2)(x22x+3)3=2(x1)(x22x+3)3
If the slope of the tangent is 0, then we have:
2(x1)(x22x+3)3=0
When x=1,y=112+3=12
the equation of the tangent through (1,12) is given by,
y12=0(x1)y=12

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