9.6 Gradients of Tangents, Equations of Tangents and Normals
If A(x1, y1) is a point on a line y = f(x), the gradient of the line (for a straight line) or the gradient of the tangent of the line (for a curve) is the value of when x = x1.
(A) Gradient of tangent at A(x1, y1):
(B) Equation of tangent:
(C) Gradient of normal at A(x1, y1):
(D) Equation of normal :
Example 1 (Find the Equation of Tangent)
Given that . Find the equation of the tangent at the point (1, 1).
Example 2 (Find the Equation of Normal)
Find the gradient of the curve at the point (-1, 7). Hence, find the equation of the normal to the curve at this point.