Question

Identify the interval where y = x3 + 3x2 - 2x + 4 is decreasing.

Answer 1

Please be certain to use the symbol "^" to denote exponentiation.  Your function y should be written as

y = x^3 + 3x2 - 2x + 4.

Principle:  if the derivative of a function is negative on a certain x-interval, the function is decreasing on that interval.      Thus, you must differentiate the given function:  find dy/dx.  Set this dy/dx = to 0 and solve the resulting equation for x.  Set up intervals on the # line based upon your solutions.
For example, if x=-1 and x=2, then set up 3 intervals:  (-infinity,-1), (-1,2), and (2, infinity).  Looking at each interval separately, identify the interval or intervals on which the derivative dy/dx is negative.  

This is a critically important skill in calculus and well worth the time and effort required to learn it.