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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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`f(x)=x^{3}-15 x^{2}+75 x-50`
` f^{prime}(x)=3 x^{2}-30 x+75 `
` =3(x^{2}-10 x+25) `
` =3(x-5)^{2}>0, forall x in R`
`
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