How do you find the equation of a tangent line in calculus? - Answers

Suppose a curve is defined by the function y = f(x) and you want the equation of the tangent at the point A.Suppose the x-coordinate at A is p. Then use y = f(p) to find the y-coordinate of A and let that be q. So, the point A is (p, q).Next, find dy/dx, the derivative of the function f, with respect to q. This will be a constant or a functio of x. In the latter case, find its value for x = p. This is m, the gradient of the tangent.So now you have the tangent line with gradient, m which passes through the point (p, q) and so its equation isy - q = m(x - p)Simplify this into the required form: y = mx + c or ax + by + c = 0.