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

using only the values given in the table for the function, f(x)=x^3 - 3x - 2, what is the interval of x - values over which the function is decreasing?\n(-4,1)\n(-4,-1)\n(-1,1)\n(-1,2)\n\nx | f(x)\n-4 | -54\n-3 | -20\n-2 | -4\n-1 | 0\n0 | -2\n1 | -4\n2 | 0\n3 | 16

using only the values given in the table for the function, f(x)=x^3 - 3x - 2, what is the interval of x - values over which the function is decreasing?\n(-4,1)\n(-4,-1)\n(-1,1)\n(-1,2)\n\nx | f(x)\n-4 | -54\n-3 | -20\n-2 | -4\n-1 | 0\n0 | -2\n1 | -4\n2 | 0\n3 | 16

Answer

Answer:

C. (-1,1)

Explanation:

Step1: Understand decreasing function

A function is decreasing when as (x) increases, (f(x)) decreases.

Step2: Check intervals

For the interval ((-4, - 1)): when (x=-4,f(x)=-54); when (x = - 1,f(x)=0), (f(x)) is increasing. For the interval ((-4,1)): from (x=-4) to (x=-1) it increases first then from (x=-1) to (x = 1) it decreases. For the interval ((-1,1)): when (x=-1,f(x)=0); when (x = 0,f(x)=-2); when (x = 1,f(x)=-4). As (x) increases from (-1) to (1), (f(x)) decreases. For the interval ((-1,2)): when (x=-1,f(x)=0); when (x = 2,f(x)=0), it decreases then increases. So the function is decreasing over the interval ((-1,1)).