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???

Jun 11, 2018

C is correct

Explanation:

The slope function will be the derivative, which is

$y ' = 3 {x}^{2} - 3$

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

$y ' ' = 6 x$

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!