Mathematics · supplementary
Tangency slope and tangent-normal basics for JEE
Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable
Formula
\[m_{\text{tangent}}=\frac{dy}{dx},\qquad m_{\text{normal}}=-\frac{1}{dy/dx}\]
Variables: Slopes at a point on the curve.
Conditions: For normal slope, tangent slope should be nonzero and finite; vertical/horizontal cases handled separately.
Application of derivative to tangents, normals, monotonic behavior near points.