The problem provided asks to find $(f - g)'(2)$ given some information about the functions $f(x)$ and $g(x)$ at $x = 2$. Here's how we can solve it:

Given:

• $f(2) = 7$
• $g(2) = 14$
• $f'(2) = 12$
• $g'(2) = 5$

To find:

$(f - g)'(2)$

Solution:

We can use the basic rule for differentiation: $(f - g)'(x) = f'(x) - g'(x)$ At $x = 2$, this becomes: $(f - g)'(2) = f'(2) - g'(2)$

Substitute the given values: $(f - g)'(2) = 12 - 5 = 7$

Thus, the answer is: $(f - g)'(2) = 7$

Would you like further details or explanations?

Here are some related questions for you to consider:

1. How do you apply the sum/difference rule for derivatives in more complex functions?
2. What would $(f + g)'(2)$ be, using the same given data?
3. What happens to the derivative when functions are multiplied? (Product rule)
4. How does the chain rule apply to composite functions involving $f$ and $g$?
5. Can you visualize the graphs of $f(x)$ and $g(x)$ based on this data?

Tip: Always verify if differentiation rules (sum, product, chain) are being correctly applied to avoid errors in more complex functions.