Question

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???

Answer 1

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!