Tangents and normals

Definitions of tangent and normal, finding tangent and normal lines to a function

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Exercises

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SL 5.4

L:mx+c is tangent to f(x) at x=a means

same ysame y′{f(a)=ma+cf′(a)=m🚫

Using point slope form the equation of the tangent is:

y−f(a) ⇒y=m⋅(x−a)🚫 =mx−ma+f(a)🚫

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SL 5.4

The normal to f(x) at x=a is the line that passes through (a,f(a)) and is perpendicular to the tangent:

mn⋅mt=−1⇔mn =−mt1🚫 =−f′(a)1🚫

Using point slope form the equation of the tangent is:

y−f(a) ⇒y=mn⋅(x−a)🚫 =mnx−mna+f(a)🚫

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SL 5.4

L:mx+c is tangent to f(x) at x=a means

same ysame y′{f(a)=ma+cf′(a)=m🚫

Using point slope form the equation of the tangent is:

y−f(a) ⇒y=m⋅(x−a)🚫 =mx−ma+f(a)🚫

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SL 5.4

The normal to f(x) at x=a is the line that passes through (a,f(a)) and is perpendicular to the tangent:

mn⋅mt=−1⇔mn =−mt1🚫 =−f′(a)1🚫

Using point slope form the equation of the tangent is:

y−f(a) ⇒y=mn⋅(x−a)🚫 =mnx−mna+f(a)🚫

Powered by Desmos