How to find the tangent line and normal line to a curve at a point
Both the graph of y = f(x) and the tangent line pass through the point, and the tangent line has the same gradient, 'm', as the function at that point. The normal line to function y = f(x) at the point (x1,y1) is the straight line that passes through the point making a 90 angle with the graph.The gradient of the normal line is -1/m, where 'm' is the gradient of the tangent line at the same point.'m' is the gradient at (x1,y1)). The equation of the normal line to y = f(x) at (x 1 ,y 1) is: The derivative of y = f(x) at (x 1 ,y 1) gives us the gradient 'm'. For example: Calculate the tangent and normal lines to the function: y = x 2, when x = 1. Solution: Part 1, tangent line.