It is given that
f(x) = x3 – 15x2 + 75 x – 50
By differentiating w.r.t x
f’(x) = 3x2 – 30x + 75
By taking 3 as common
f’(x) = 3(x2 – 10x + 25)
On further simplification
f’(x) = 3(x – 5)2
Here f’(x) ≥ 0 for all x ≥ 0
Therefore, f(x) is increasing function on R.