How do you know if a line is tangent to a curve?
Please check the explanation.
By solving the two equations you will get a point
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
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
1) Finding the intersection point :
by solving the two equation the intersection point will be
2) Finding the first derivative of the curve function:
By substituing with the value of
Which is equal to the slope of the straight line