The slope of the line tangent to the graph y = f(x) at the point (a,f(a)) is the derivative f0(a) = lim h→0 f(ah)−f(a) h, of y = f(x) at (a,f(a)), if it exists Example 3 We saw in Example 2 that the derivative of f(x) = x 2at x = 3 is f0(3) = 6, so the line tangent to the parabola y = x at the point (3,f(3)) = (3,9) is y = 6(x−3)9
