8. The slope of the curve y=x³-3x+1; - infinity < x <infinity is minimum at: A. X= - 1 B. X= 1 C. X=0 D. X= +1,-1 Ans. C Please give explanation???

1 Answer
Noah G
Jun 11, 2018

C is correct

Explanation:

The slope function will be the derivative, which is

#y' = 3x^2 - 3#

The minimum slope will be found by differentiating the slope function and finding the critical points.

#y'' = 6x#

This will have one critical point at #x = 0#. At #x= -1#, the slope function's derivative is negative and at #x = 1# it's positive (the function goes from decreasing to increasing), so #x = 0# is indeed a minimum.

Therefore #x =0# is where the minimum slope occurs.

Hopefully this helps!

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