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Show that f(x)=x^3-15 x^2+75 x-50 is an ...

Show that `f(x)=x^3-15 x^2+75 x-50` is an increasing function for all `x in R` .

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Given as `f(x) = x^3 – 15x^2 + 75x – 50`
` f'(x) = (d/dx)(x^3 – 15x^2 + 75x – 50)`
` ⇒ f’(x) = 3x^2 – 30x + 75`
` ⇒ f’(x) = 3(x^2 – 10x + 25)`
` ⇒ f’(x) = 3(x – 5)^2`
As given `x in R`
` ⇒ (x – 5)^2 > 0`
` ⇒ 3(x – 5)^2 > 0` ...
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