Let (x0,y0) be a point on the graph f(x) = x2 for x0 not equal to 0. Find the equation of the line tangent to the graph of f at that point by finding a line that intersects the cure in exactly one point. Do not use the derivative to find this line.
f(x) = x2
(y1-y2) = m(x1-x2)
The Attempt at a Solution
The way I would normally approach this problem is to use the derivative. But that is a syntax error in this problem; however, it does not stop me from knowing that the slope should depend on x0, where the slope of some x0 should be 2*x0.
At the same time, any point on the graph can be given in the form (x0,(x0)2). I tried to force through on this point, and get an equation (y- (x0)2) = m(x-x0). I would think I need to solve for m, but then there are too many variables, and I get too many possible solutions.
Also, I tried to set x2 = m*x + b, to see the set of solutions. That is unhelpful, there are solutions to that set of equations that are not tangents to the graph, but instead are secants.
I believe that my general approach to the problem is wrong; I am missing something. I would love any advice.