What is the least value of $f(x) = 2 x^{3} - 9 x^{2} + 12 x + 1$ on $[0, 3]$?

Explanation

1. 01

   Critical points inside the interval: $f'(x) = 6 \left(x - 2\right) \left(x - 1\right) = 0$ at $x = 1, 2$.

2. 02

   Compare $f$ there and at the two ends: $f(0) = 1$, $f(3) = 10$, $f(1) = 6$, $f(2) = 5$.

3. 03

   The least value is $1$.