How do you know if a line is tangent to a curve?

1 Answer
Yahia M.
Apr 2, 2018

Please check the explanation.

Explanation:

By solving the two equations you will get a point #(x,y) # which lies on both the curve and the straight line.
if you got more than one point then this line will be intersecting and not a tangent to the curve.
then by finding the first derivative of the curve and substituting with the value of the point#(x,y)#
if it's value is equal to the slope of the straight line then this line is its tangent.

For example :
determine whether the line #y=2x-1# is a tangent to the curve #y=x^2#

1) Finding the intersection point :
by solving the two equation the intersection point will be #(1,1)#

2) Finding the first derivative of the curve function:
#y=x^2#
#y'=2x#
By substituing with the value of #x=1#
#y'=2#
Which is equal to the slope of the straight line #y=2x-1#

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