[PDF] Mathematics Notes for Class 12 chapter 6 Application of Derivatives

16223_2MathsNotesforClass12chapter6_ApplicationofDerivatives.pdf

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Mathematics Notes for Class 12 chapter 6.

Application of Derivatives

Tangents and Normals

of the tangent to the curve at P is where (x, y) is an arbitrary point on the tangent.

The equation of normal at (x, y) to the curve is

1. If then the equations of the tangent and normal at (x, y) are (Y

y) = 0 and (X x) = 0, respectively.

2. If then the equation of the tangent and normal at (x, y) are (X x)

= 0 and (Y y) = 0, respectively.

Slope of Tangent

(i) If the tangent at P is perpendicular to x-axis or parallel to y-axis,

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(ii) If the tangent at P is perpendicular to y-axis or parallel to x-axis,

Slope of Normal

(ii) If , then normal at (x, y) is parallel to y-axis and perpendicular to x-axis. (iii) If then normal at (x, y) is parallel to x-axis and perpendicular to y-axis.

Length of Tangent and Normal

(i) ș = (ii) Length of normal, (iii) Length of subtangent, (iv) Length of subnormal,

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Angle of Intersection of Two Curves

Let y = f1(x) and y = f2(x) be the two curves, meeting at some point P (x1, y1), then the angle between the two curves at P (x1, y1) = The angle between the tangents to the curves at P (x1, y1) The other angle between the tangents is (180 ș is taken to be the angle of intersection. ׵

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Derivatives as the Rate of Change

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