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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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