I have figured out (c) and (d) for you. Maybe someone else that knows more can help you with (e) and (f).
f' = (4x^3 - 36x)/5
To figure out where its decreasing or increasing, we need to find the critical point. Which is found by setting the first dervative equal to 0, and then solving for x.
0 = (4x^3 - 36x)/5
0 = x(4x^2 - 36)
0 = x(2x+6)(2x-6)
So x = 0, x = -3, x = 3 are our options.
To classify them as a critical point we need to test points within our critical points, and observe the behavior when we plug them into f'(x)... observing meaning just check whether they are + or -
f'(-4) = -
f'(-1) = +
f'(1) = -
f'(4) = +
So we are decreasing from x = -∞ to x= -3
Then increasing from x = -3 to x = 0
Then decreasing from x= 0 to x = 3
Then increasing from x = 3 to x = ∞
So our interval of decreasing:
(-∞, -3] U [0, 3]
And our interval of increasing:
[-3, 0] U [3, ∞)