Question
Find all points at which the graph of f (x) = x^3 −3x has horizontal tangent lines.
Answers
Reiny
f'(x) = 3x^2 - 3
= 0 for a horizontal tangent
3x^2 = 3
x^2 = 1
x = ± 1
if x=1, f(1)= 1-3 = -2
if x=-1 , f(-1) = -1+3 = 2
points are (1,-2) and (-1,2)
= 0 for a horizontal tangent
3x^2 = 3
x^2 = 1
x = ± 1
if x=1, f(1)= 1-3 = -2
if x=-1 , f(-1) = -1+3 = 2
points are (1,-2) and (-1,2)