For f(x) =(x-1)^3f(x)=(x1)3, what is the equation of the line tangent to x =2 x=2?

1 Answer
Nov 20, 2015

y =3*x -5y=3x5

Explanation:

f(x) =(x-1)^3f(x)=(x1)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