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Prove that the Function F ( X ) = X 3 − 6 X 2 + 12 X + 5 is Increasing on R. - Mathematics

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Sum

 Prove that the function `f(x) = x^3- 6x^2 + 12x+5` is increasing on R. 

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Solution

`f(x)=x^3 - 6X^2 + 12x +5;`        x ∈ R
`f'(x)=3x^2- 12x+12;`                  x ∈ R
`f'(x) = 3(x^2 - 4x + 4)=3(x-2)^2`; x ∈ R
∴ f'(x)≥ 0 ;  x ∈ R
∴ f'(x) is increasing for x ∈ R

Concept: Increasing and Decreasing Functions
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