JEE • Mathematics

Application of Derivatives

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mixed

Tangent and Normal Equations

The source gives tangent and normal at (x1,y1)(x_1,y_1) on y=f(x)y=f(x).

y−y1=f′(x1)(x−x1)y-y_1=f'(x_1)(x-x_1)
y−y1=−1f′(x1)(x−x1)y-y_1=-\frac{1}{f'(x_1)}(x-x_1)

Variables & Notation

ff

function

Notes

  • Tangent formula requires f′(x1)f'(x_1) real.

  • Normal formula requires f′(x1)f'(x_1) nonzero real.