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Calculus/Critical Numbers

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Expert: - 7/22/2010


Question
What are the Critical numbers of |X2 - 1|

Answer

Graph
Hi Simon,
|x²-1| = x²-1 when x²-1 > 0 i.e x < -1 and x < 1
AND
|x²-1| = -(x²-1) = 1-x² when x²-1 < 0 i.e -1 < x < 1

The critical point of x²-1 occurs when its derivative is equal to zero, i.e
2x = 0
x = 0
The critical point of -(x²-1) occurs when its derivative is equal to zero, i.e
-2x = 0
x = 0
Now, both x²-1 and -(x²-1) change sign at x = -1 and x = 1
So, the critical values are;
x = -1, 0, 1

NB: See attached image.

Regards
    Questioner's Rating
    Rating(1-10)Knowledgeability = 10Clarity of Response = 10Politeness = 10
    CommentThanks a lot Mr. Ahmed that was a great help.


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Ahmed Salami

Expertise

I can provide good answers to questions dealing in almost all of mathematics especially from A`Level downwards. I believe i would be very helpful in calculus and can as well help a good deal in Physics with most emphasis directed towards mechanics.

Experience

An engineering graduate. I have been doing maths and physics all my life.

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