Using only the values given in the table for the function f(x) = –x3 + 4x + 3, what is the largest interval of x-values where the function is increasing?

The values are the given below:

Table

x           f(x) = - x^3 + 4x + 3

-3          -(-3)^3 + 4(-3) + 3 = 27 - 12 + 3 = 18

-2         -(-2)^3 + 4(-2) + 3 = 8 - 8 + 3 = 3

-1         -(-1)^3 + 4(-1) + 3 = 1 - 4 + 3 = 0

0           0^3 + 4(0) + 3 = 3

1           -(1)^3 + 4(1) + 3 = - 1 + 4 + 3 = 6

2           -(2)^3 + 4(2) + 3 = -8 + 8 + 3 = 0

So, the interval in which the values are increasing is (-1,1), because the function increases from 0 to 3 to 6.

(-1,1)