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Example 8 - Show f(x) = x3 - 3x2 + 4x is strictly increasing

Example 8 - Chapter 6 Class 12 Application of Derivatives - Part 2

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Example 8 Show that the function f given by f (π‘₯) = π‘₯3 – 3π‘₯2 + 4π‘₯, π‘₯ ∈ R is strictly increasing on R. f(π‘₯) = π‘₯3 – 3π‘₯2 + 4π‘₯ Finding f’(𝒙) f’(π‘₯) = 3π‘₯2 – 3.2π‘₯ + 4 f’(π‘₯) = 3x2 – 6π‘₯ + 4 f’(π‘₯) = 3x2 – 6π‘₯ + 3 + 1 f’(π‘₯) = 3 (π‘₯2 – 2π‘₯ + 1) + 1 f’(𝒙) = 3 (𝒙 – 1)2 + 1 As square is a positive number, The value of f’(π‘₯) will be always positive for every real number Hence f’(𝒙) > 0 for all π‘₯ ∈ R ∴ f(π‘₯) is strictly increasing

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