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