Show that the function f given by f(x) = x3 – 3x2 + 4x, x R is in… - Vidyadip

Question

Show that the function f given by f(x) = x³ – 3x² + 4x, x $\in$ R is increasing on R.

✓

Answer

Not that
f ′(x) = 3x² – 6x + 4
= 3(x² – 2x + 1) + 1
= 3(x – 1)² + 1 > 0, in every interval of R
Therefore, the function f is increasing on R.

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