Question 1.P.1: Find the equation of the tangent line to the parabola y = x²......

Find the equation of the tangent line to the parabola y = x² at the point (3,9) .

Let Q = ( x, x²) be another point on the graph of the parabola y = x² . The slope of the line joining (3,9) and (x,x²) is m=\frac{x^{2}-9}{x-3}=\frac{\left(x-3\right)\left(x+3\right)}{x-3}=x+3,x\neq3\;. As Q approaches (3,9), x approaches 3 , and the slope approaches 6. Hence the slope of the tangent line is 6, and the equation becomes y-9=6(x-3), or y=6x-9.