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Question

Set up an equation of a tangent to the graph of the following function.
y=x22x at the points of its intersection with the abscissa axis.

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Solution

y=x22x
To find out the point where the curve intersects abscissa is y=0
x22x=0
x(x2)=0
x=0,2
dydx=2x2
(dydx)x=0=2=m1
(dydx)x=2=2=m2
(x1,y1)=(0,0),(x2,y2)=(2,0)
(xx1)m1=yy1
2x+y=0 is the tangent at (0,0)
(xx2)m2=yy2
(x2)2=y0
2xy4=0 is the tangent at (2,0)

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