Tangents and Normals
The derivative of the curve y = f( x) is f ‗( x) which represents the slope of tangent and equation 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,
( ii) If the tangent at P is perpendicular to y-axis or parallel to x-axis,