EXAMPLE 1 Find an equation of the tangent line to the parabola y = 3x2 at the point P(1, 3) using this definition. SOLUTION Here we have a = 1, and f(x) = 3x2, so the slope is m = lim f( x) - f( 1 ) x - 1 x - 1 = lim x - 1 X - 1 = lim 3 (x - 1) ( x - 1 X - 1 = lim 3 x - 1 + 3 = Using the point slope form of the equation of a line, we find an equation of the tangent line at (1, 3) is y - ( x - or y = x