SOLUTION: f(x) = x^3 - 12x - 1 Find all values of x for the given function where the tangent line is horizontal. f(x)=(x/x^2+3)^3

Algebra ->  Equations -> SOLUTION: f(x) = x^3 - 12x - 1 Find all values of x for the given function where the tangent line is horizontal. f(x)=(x/x^2+3)^3       Log On


   

Question 881138: f(x) = x^3 - 12x - 1
Find all values of x for the given function where the tangent line is horizontal.
f(x)=(x/x^2+3)^3
Found 2 solutions by ewatrrr, Fombitz:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
f(x) = x^3 - 12x - 1
f'(x) = 3x^2 - 12 = 0, x^2 = 4, x = ± 2

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Tangent line is horizontal means the value of the derivative is zero since the derivative is the value of the slope of the tangent line.
Take the derivative and set it to zero.
df%2Fdx=3x%5E2-12
3x%5E2=12
x%5E2=4
x=0+%2B-+2
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