Prove that f(x) = x3 – 3x2 + 3x – 100 is increasing on R.

1.	Prove that f(x) = x3 – 3x2 + 3x – 100 is increasing on R.
Answer» f(x) = x³ – 3x² + 3x – 100 f'(x) = 3x² – 6x + 3 = 3(x² – 2x + 1) = 3 (x – 1)² For all values of x ∈ R, f'(x) ≥ 0, so f(x) is increasing on R.

Answer»

f(x) = x³ – 3x² + 3x – 100

f'(x) = 3x² – 6x + 3 = 3(x² – 2x + 1) = 3 (x – 1)²

For all values of x ∈ R, f'(x) ≥ 0, so f(x) is increasing on R.

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Prove that f(x) = x3 – 3x2 + 3x – 100 is increasing on R.

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