Tangents and normals

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

Read this first:Differentiation rules

This lesson will teach you how to

Determine the gradient of a tangent to a curve at a given point using the derivative.

Tangent to f(x)

SL 5.4

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

same ysame y′{f(a)=ma+cf′(a)=m

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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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Normal to f(x)

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

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Using point slope form the equation of the tangent is:

y−f(a) ⇒y=mn⋅(x−a) =mnx−mna+f(a)

🚫🚫

Nice work completing Tangents and normals, here's a quick recap of what we covered:

Skills covered

Mixed Practice

Exercises checked off

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Applications of the First Derivative

Differentiation

Tangents and normals

0 of 0 checkpoints completed

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

Read this first:Differentiation rules

This lesson will teach you how to

Determine the gradient of a tangent to a curve at a given point using the derivative.

Tangent to f(x)

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)

🚫🚫

Normal to f(x)

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)

🚫🚫

Nice work completing Tangents and normals, here's a quick recap of what we covered:

Skills covered

Mixed Practice

Exercises checked off

I'm Plex, here to help you understand this concept!

1 free

Find the equation of a tangent to a curve at a given point.

Understand that the normal to a curve is perpendicular to the tangent at the point of contact.

Determine the gradient of a normal using mnormal=−mtangent1.

Find the equation of a normal to a curve at a given point.