SOLUTION: Question The points on the curve y = x3 - x2 - x + 1, where the tangent is parallel to x-axis are 1. (1, 0), (- 1/3, 32/27) 2. (1, 0), (1, 1) 3. (- 1/3, 21/37), (0, 0)

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Question 974073: Question
The points on the curve y = x3 - x2 - x + 1, where the tangent is parallel to x-axis are

1. (1, 0), (- 1/3, 32/27)
2. (1, 0), (1, 1)
3. (- 1/3, 21/37), (0, 0)

Answer Explanation : y = x3-x2-x+1
Thus by putting value, this answer is correct.

Found 2 solutions by Alan3354, Boreal:
Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
The points on the curve y = x3 - x2 - x + 1, where the tangent is parallel to x-axis are
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Find the 1st derivative:
f'(x) = 3x^2 - 2x - 1
Parallel to the x-axis --> slope = 0 --> f'(x) = 0
3x^2 - 2x - 1 = 0
(3x + 1)*(x - 1) = 0
x = -1/3, x = 1

Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website!
Take the first derivative:
3x^2-2x-1.
Tangent has 0 slope if parallel to x-axis.
3x^2-2x-1=0
(3x+1)(x-1)=0
x=1, x= -(1/3)
x=1; y=0 in original equation
x=(-1/3) ;; y=(-1/27)-(1/9)+(1/3) +1 = (32/27)