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Show that function f given by f(x)=(1)/(...

Show that function f given by `f(x)=(1)/(5)x^(5)-3x^(4)+12x^(3)+4x, x in R ` is stictly increasing on R.

Text Solution

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Note that ` f'(x)=x^(4)-12x^(3)+36x^(2)+4`
`=x^(2)(x^(2)-12x+36)+4 `
`=x^(2)(x-6)^(2)+4 `
As , `f'(x) gt 0` for `AA x in R `
Therefore , f is strictly increasing on R .
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