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## Homework Statement

Let (x

_{0},y

_{0}) be a point on the graph f(x) = x

^{2}for x

_{0}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.

## Homework Equations

f(x) = x

^{2}

y=mx+b

(y

_{1}-y

_{2}) = m(x

_{1}-x

_{2})

## 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 x

_{0}, where the slope of some x

_{0}should be 2*x

_{0}.

At the same time, any point on the graph can be given in the form (x

_{0},(x

_{0})

^{2}). I tried to force through on this point, and get an equation (y- (x

_{0})

^{2}) = m(x-x

_{0}). 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 x

^{2}= 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.