using only the values given in the table for the function, ( f(x)=x^{3}-3x - 2 ), what is the interval…

using only the values given in the table for the function, ( f(x)=x^{3}-3x - 2 ), what is the interval ofvalues over which the function is decreasing?\n( (-4,1) )\n( (-4,-1) )\n( (-1,1) )\n( (-1,2) )

using only the values given in the table for the function, ( f(x)=x^{3}-3x - 2 ), what is the interval ofvalues over which the function is decreasing?\n( (-4,1) )\n( (-4,-1) )\n( (-1,1) )\n( (-1,2) )

Answer

Explanation:

Step1: Analyze the function values

A function (y = f(x)) is decreasing if when (x_1<x_2), (f(x_1)>f(x_2)).

  • For the interval ((-4,1)):
    • When (x=-4), (f(-4)=-54); when (x = - 3), (f(-3)=-20), (-54<-20) (function is increasing in part of this interval).
  • For the interval ((-4,-1)):
    • When (x=-4), (f(-4)=-54); when (x=-3), (f(-3)=-20), (-54<-20) (function is increasing in part of this interval).
  • For the interval ((-1,1)):
    • When (x=-1), (f(-1) = 0); when (x = 0), (f(0)=-2) ((0>-2)); when (x = 1), (f(1)=-4) ((-2>-4)).
  • For the interval ((-1,2)):
    • When (x = 1), (f(1)=-4); when (x = 2), (f(2)=0), (-4<0) (function is increasing in part of this interval).

Answer:

((-1,1))