EXAMPLE 1 Find an equation of the tangent line to the parabola y = 5x at the point P(4, 80) using this definition. SOLUTION Here we have a = 4, and /(x) = 5x , so the slope is m = lim f(x) - 14) X - 4 x - 4 = lim 5x- - 5(4) 2 X - 4 X - 4 = lim 5(x - 4) x - 16 X - 4 X X - 4 = lim 5 x+4 X -4 = 5( 4) + 20 = 40 Using the point slope form of the equation of a line, we find an equation of the tangent line at (4, 80) is Y 40 (x - 4 ) or y= 40 80