Home/Differential Calculus/Derivative and geometric interpretation/Tangent and normal linesSection 4.2Tangent and normal linesFormulavizCopy LaTeXy−f(a)=f′(a)(x−a)y-f(a)=f'(a)(x-a)y−f(a)=f′(a)(x−a)Tangent line to y=f(x)y=f(x)y=f(x) at x=ax=ax=a.View detail →FormulavizCopy LaTeXy−f(a)=−1f′(a)(x−a),f′(a)≠0y-f(a)=-\frac{1}{f'(a)}(x-a),\qquad f'(a)\neq0y−f(a)=−f′(a)1(x−a),f′(a)=0Equation of the normal line.f′(a)≠0f'(a)\neq0f′(a)=0View detail →FormulaCopy LaTeXmtan=f′(a)m_{\mathrm{tan}}=f'(a)mtan=f′(a)Slope of the tangent.View detail →
FormulavizCopy LaTeXy−f(a)=f′(a)(x−a)y-f(a)=f'(a)(x-a)y−f(a)=f′(a)(x−a)Tangent line to y=f(x)y=f(x)y=f(x) at x=ax=ax=a.View detail →
FormulavizCopy LaTeXy−f(a)=−1f′(a)(x−a),f′(a)≠0y-f(a)=-\frac{1}{f'(a)}(x-a),\qquad f'(a)\neq0y−f(a)=−f′(a)1(x−a),f′(a)=0Equation of the normal line.f′(a)≠0f'(a)\neq0f′(a)=0View detail →