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

Answer 1

Please check the 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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Answer 2

Emily Ammerman

A line is tangent to a curve if it touches the curve at exactly one point and has the same slope as the curve at that point.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.