# 2.6 Gradients of Tangents, Equations of Tangents and Normals

2.6 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 $\frac{dy}{dx}$ 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 $y=\frac{4}{{\left(3x-1\right)}^{2}}$ . Find the equation of the tangent at the point (1, 1).

Solution:

Example 2 (Find the Equation of Normal)
Find the gradient of the curve $y=\frac{7}{3x+4}$ at the point (-1, 7). Hence, find the equation of the normal to the curve at this point.

Solution: