For $f (x) = {(x - 1)}^{3}$ $f(x) =(x-1)^3$ , what is the equation of the line tangent to $x = 2$ $x =2$ ?

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Answer 1 · 2015-11-20T19:57:45

$y = 3 \cdot x - 5$ $y =3*x -5$

$f (x) = {(x - 1)}^{3}$ $f(x) =(x-1)^3$

Derive the function:
$f'(x)=3*(x-1)^2$

Insert x=2
$f'(2)=3*(2-1)^2=3$

The derivative in x =2 is the slope of the tangent.

Calculate the value of the function in x=2
$f(2)=(2-1)^3=1^3=1$

The tangent intersects the point (2,1)

the equation of the tangent
$y = k*x +m$
$k=3$

$y = 3*x + m$
$1 = 3*2 + m$
$m =1-6=-5$

$y =3*x -5$

For f(x) =(x-1)^3f(x)=(x−1)3f(x) =(x-1)^3, what is the equation of the line tangent to x =2 x=2x =2 ?