Final answer:
The interval(s) on which the function f(x) = 2x³ + 3x² - 120x is increasing are (-∞, -5) and (4, +∞).
Step-by-step explanation:
To find the interval(s) on which the function f(x) = 2x³ + 3x² - 120x is increasing, we need to determine where the derivative of the function is positive. The derivative of f(x) with respect to x is f'(x) = 6x² + 6x - 120. To find the critical points, we set f'(x) = 0 and solve for x. We can factor out a 6 from the equation to simplify it: 6(x² + x - 20) = 0. By factoring the quadratic equation, we get (x + 5)(x - 4) = 0. So, the critical points are x = -5 and x = 4.
Now, we can test the intervals between the critical points and beyond to determine the sign of the derivative and whether f(x) is increasing or decreasing. Using a sign chart or plugging in test values, we find that f'(x) > 0 for x < -5 and -5 < x < 4. Therefore, the interval(s) on which f(x) is increasing are (-∞, -5) and (4, +∞).