Question

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

Answer 1

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`