# At what points on the graph of #y = x^2# does the tangent line pass through (3, −7)?

##### 1 Answer

The points are

Method: Find the general form of the equation of a line tangent to the graph of

I will continue to use

Consider a particular value of

The point an the graph at

The slope of the tangent to the graph is determined by differentiating:

Use your favorite tehnique to find the equation of the line through

The tangent line has equation:

(One way to find the line: start with

We have been asked to make the point

Solve by factoring:

The points we are looking for, then, are

You can now check the answers by verifying that the point

and also on