Tangent through point touching function


You have a point with coordinates and a function . does not lie on the graph of . What is the equation of a tangent that touches and goes through the point ?
If you use the Tangent command with the point and the function as an argument, you only get a tangent to the function at a new point that has the same coordinate and lies on the graph of . This is not what we want to achieve. But there is a trick so we can get our tangent(s). The Tangent command has a version with a point and an implicit function as arguments. This works as we want to. So we convert our function f(x) into an implicit equation with and then use the Tangent command. Sometimes it is necessary to zoom out to get more tangents. See the following applet