The image appears to describe a math problem. Let me extract and break it down for you:

The problem is:

Given that $g(x) = 3x + 5$ and $f(x) = ax^2 - bx^3 + cx$ intersect at an inflection point, and that the function $f$ has an inflection point at $(1, 8)$, find the values of $a$, $b$, and $c$.

To solve this:

1. Inflection point: An inflection point occurs where the second derivative of the function is zero.
2. Intersection of functions: For the functions $g(x)$ and $f(x)$ to intersect at the inflection point, they must have the same value and slope at the point of intersection.

We'll need to:

• Use the second derivative of $f(x)$ to confirm the inflection point.
• Solve the system of equations that come from the conditions given (value at $(1, 8)$, slopes being equal, etc.).

Let me work through the necessary steps. Would you like me to go into the details of solving this system?