Find the equation of the tangent line to y = x^2 at x = 3

Problem: Find the equation of the tangent line to $y = x^2$ at $x = 3$.

Steps

1. Find the derivative
   $$\frac{dy}{dx} = 2x$$
2. Evaluate the derivative at the given point to find the slope
   $$m = 2(3) = 6$$
3. Find the y-coordinate of the point of tangency
   $$y_0 = 3^2 = 9$$
4. Use the point-slope form with point $(3, 9)$ and slope $m = 6$
   $$y - 9 = 6(x - 3)$$
5. Simplify into slope-intercept form
   $$y = 6x - 9$$