Find the intervals of increasing and decreasing of the function f (x) = 60 + 45x-3x ^ 2-x ^ 3

To find the intervals of monotonicity of the function (increase or decrease), we calculate the derivative and find its roots, we get:

f ‘(x) = 45 – 6 * x – 3 * x²,

f ‘(x) = 0,

45 – 6 * x – 3 * x² = 0.

The roots of the quadratic equation are:

x = 3,

x = -5.

The function increases in the interval [-5; 3] (the derivative is positive), decreases on the intervals (-∞; -5] and [3; + ∞) (the derivative is negative).