Question

Using only the values given in the table for the function, f(x) = x3 – 3x – 2, what is the interval of x-values over which the function is decreasing?

(–4, 1)(–4, –1)(–1,1) (–1, 2)

Answer 1

Given:

f(x) = x^3 - 3x - 2 and the values in the table attached.

The interval of x-values over which the function is decreasing is from x = -1 to x = -4. The function decreases from f(x) = 0 to f(x) = -54. Therefore, the solution set is (-4, -1)

Answer 2

Hence, the interval in which function f(x) is decreasing is:

(-1,1)

Explanation:

We have to find the intervals on which the function f(x) is decreasing.

i.e. with the increasing value of x the function f(x) must decrease or we can say the value of f(x) decreases with the increasing value of x.

Clearly from the set of values given we can see that the function f(x) decreases in the interval:

(-1,1) ( since at x=-1 f(x)=0

and at x=1 f(x)=-4 )

Hence, the interval is:

(-1,1)