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Tangent Line

Tags
Calculus
Cegep/1
Word count
162 words
Reading time
2 minutes

Line that touches a curve at exactly one point

The slope of the tangent line at (a,f(a)) to the curve given by y=f(x) is

limxaf(x)f(a)xa

[!example]- Find the equation of the tangent to the curve y=x2+2x at x=1.
The equation of the tangent is

yyo=m(xxo)

where

m=limxaf(x)f(a)xa=limx1x2+2x3x1=limx1(x1)(x+3)x1=limx1(x+3)=4

Since the tangent shares the point (1,f(1))=(1,3) with f,

y3=4(x1)y=4x4+3y=4x1

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