Question

find all points on the curve y=x^3-3X where the tangent is parallel to the x-axis.

Answer 1

this should be intuitive because tangent parallel to the x-axis implies that its value is 0. And then you find the prime of y, and set it to 0

Answer 2

tangent is parallel to the x-axis so its slope equals to 0.
on the other hand slope of tangent line equals to derivative of function at the given point