Find the intervals on which f(x) = 2x³ - 9x² + 12x + 5 is increasing and decreasing…

Step 1. The derivative. $f'(x) = 6x^2 - 18x + 12 = 6(x - 1)(x - 2)$.

Step 2. The turning values. $f'(x) = 0$ at $x = 1$ and $x = 2$.

Step 3. The signs. At $x = 0$, $f' = 12 > 0$. At $x = 1.5$, $f' = 6(0.5)(-0.5) = -1.5 < 0$. At $x = 3$, $f' = 6(2)(1) = 12 > 0$.

Step 4. The values. $f(1) = 2 - 9 + 12 + 5 = 10$ and $f(2) = 16 - 36 + 24 + 5 = 9$.