The problem presented in the image is:

Given $f(x) = x^3 - 3x^2 + 2x - 5$, what is $f(2) - f(3)$?

Let's solve this step by step.

1. Find $f(2)$:

$f(2) = 2^3 - 3(2)^2 + 2(2) - 5$ $f(2) = 8 - 12 + 4 - 5 = -5$

2. Find $f(3)$:

$f(3) = 3^3 - 3(3)^2 + 2(3) - 5$ $f(3) = 27 - 27 + 6 - 5 = 1$

3. Calculate $f(2) - f(3)$:

$f(2) - f(3) = -5 - 1 = -6$

Therefore, the correct answer is $-6$, which corresponds to the option with $-6$.

Would you like further details or have any questions? Here are some related questions to consider:

1. What is the significance of the cubic term in $f(x)$?
2. How does changing the coefficient of the quadratic term affect the graph of $f(x)$?
3. What would $f(x) - f(y)$ represent geometrically?
4. How can the remainder theorem be applied to evaluate $f(2)$ and $f(3)$?
5. What happens to $f(x)$ as $x$ approaches infinity?

Tip: When dealing with polynomial functions, always carefully substitute values step-by-step to avoid mistakes.