Calculus Question

Question

The slope of the tangent to y = x^3-x at x =1 is 2. Determine the equations of the tangent and normal lines at that point. 

 

Please help!?

Answer 1

y = mx + b

 

y = 2x + b

 

f(1) = 1³ - 1 = 0

 

0 = 2(1) + b

 

b = -2

 

Tangent line: y = 2x - 2 

 

For the normal line:

 

m = -1/2 (recall that slopes of perpendicular lines obey m₁m₂ = -1)

 

y = (-1/2)x + b

 

At the same point (1, f(1)),

 

0 = (-1/2)(1) + b

 

b = 1/2

 

Normal line:  y = (-1/2)x + 1/2