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Show that f(x) = x3 – 15x2 + 75x – 50 is increasing on R.

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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.

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