Question

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? $(-4,1)$ $(-4,-1)$ $(-1,1)$ $(-1,2)$

Explanation:

Step1: Check function trend from x=-4 to x=-1

f(-4)=-54, f(-3)=-20, f(-2)=-4, f(-1)=0: values increase.

Step2: Check trend from x=-1 to x=1

f(-1)=0, f(0)=-2, f(1)=-4: values decrease.

Step3: Check trend from x=1 to x=3

f(1)=-4, f(2)=0, f(3)=16: values increase.

Step4: Identify decreasing interval

Decreasing between x=-1 and x=1.

Answer:

(-1,1)