For the given function f and value a, find the tangent line to f at a.
We need a point and a slope. Since a = 1 and , the point we want is . We found earlier that . We want a line
y = mx + b
whose slope is , so
We want the point to be on the line, so
Solving, we find so the equation of the tangent line is
We can check this with a picture: