To find the value of $f(0)$ for the function $f(x) = -2x^3 + 3x^2 - 11x + 1$, substitute $x = 0$ into the function:

$f(0) = -2(0)^3 + 3(0)^2 - 11(0) + 1$

Simplifying the terms:

$f(0) = 0 + 0 + 0 + 1 = 1$

Therefore, the value of $f(0)$ is $\boxed{1}$.

Would you like more details, or do you have any questions?

Here are 5 related questions:

1. What is $f(1)$ for the same function?
2. How would you find the roots of $f(x) = 0$?
3. What is the derivative $f'(x)$ of this function?
4. Can you find the turning points of $f(x)$?
5. What is the end behavior of $f(x)$ as $x \to \infty$?

Tip: When substituting values into functions, always replace $x$ with the given number carefully in each term.