NTA CUET Mathematics With Fully Solved 2023 Papers by Pearson

CHAPTER 3

Differentiation and its Application

CHAPTER AT A GLANCE

Tangent and Normal

Let y = f(x) be a function with a graph as shown in the figure. Consider secant PQ. If Q tends to P along the curve passing through the points Q₁, Q₂, … i.e., Q → P, secant PQ will become tangent at P. A line through P perpendicular to the tangent is called normal at P.

Geometrical Meaning of

As Q → P, h → 0 and slope of chord PQ tends to slope of the tangent at P (see figure).

Slope of chord PQ =

slope of chord PQ =

⇒ slope of tangent at P = f ′(