Which table describes the behavior of the graph of f (x) = 2x3 - 26x - 24?

2 x³ - 26 x - 24 = 0

2 x³ - 2 x - 24 x - 24 = 0

2 x (x² - 1) - 24 (x + 1) = 0

2 x (x + 1) (x - 1) - 24 (x + 1) = 0

(x + 1) (2 x² - 2 x - 24) = 0

x 1 = - 1;

2 x² - 2 x - 24 = 0 / : 2

x² - x - 12 = 0

x² - 4 x + 3 x - 12 = 0

x (x - 4) + 3 (x - 4) = 0

(x - 4) (x + 3) = 0

x 2 = 4, x 3 = - 3;

The zeroes are : { - 3, - 1, 4 }.

The function : f (x) = a x³ (where a > 0) first goes up.

Answer:

B) For x ∈ ( - ∞, - 3) y < 0 (below the x-axis);

x ∈ ( - 3, - 1) y > 0;

x ∈ ( - 1, 4) y < 0;

x ∈ (4, + ∞) y > 0 (above the x-axis).