To solve the expression $2f(-3) - f(4)$ for the function $f(x) = 3x^2 - x + 5$, follow these steps:

Step 1: Evaluate $f(-3)$

Substitute $x = -3$ into the function: $f(-3) = 3(-3)^2 - (-3) + 5 = 3(9) + 3 + 5 = 27 + 3 + 5 = 35$

Step 2: Evaluate $f(4)$

Substitute $x = 4$ into the function: $f(4) = 3(4)^2 - 4 + 5 = 3(16) - 4 + 5 = 48 - 4 + 5 = 49$

Step 3: Compute $2f(-3) - f(4)$

Now use the values found in Steps 1 and 2: $2f(-3) - f(4) = 2(35) - 49 = 70 - 49 = 21$

Final Answer:

$2f(-3) - f(4) = 21$

Would you like any additional details on these steps?

Here are five related questions:

1. How would you find the derivative of $f(x) = 3x^2 - x + 5$?
2. What happens to the expression if $f(x)$ changes to a different quadratic function?
3. How would the process change if you were given $3f(-3) - 2f(4)$?
4. How do you solve for $x$ when $f(x) = 0$ for this function?
5. Can you generalize $2f(a) - f(b)$ for any values of $a$ and $b$?

Tip: Always substitute values carefully and simplify step by step to avoid mistakes.