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To solve this limit, we'll compute the derivative of the function at the given point using the definition of a derivative. The expression provided is:

\[
\lim_{{h \to 0}} \frac{{3(2 + h)^2 + 2 - 14}}{h}
\]

Let's go through the steps to solve this:

1. **Expand the expression inside the limit:**

   \[
   3(2 + h)^2 + 2 - 14
   \]

2. **Simplify the numerator:**

   \[
   3(4 + 4h + h^2) + 2 - 14
   \]

   \[
   12 + 12h + 3h^2 + 2 - 14
   \]

   \[
   12 + 12h + 3h^2 - 12
   \]

   \[
   12h + 3h^2
   \]

3. **Factor out \( h \) from the numerator:**

   \[
   \frac{{h(12 + 3h)}}{h}
   \]

4. **Cancel the \( h \) in the numerator and the denominator:**

   \[
   \lim_{{h \to 0}} (12 + 3h)
   \]

5. **Take the limit as \( h \) approaches 0:**

   \[
   12 + 3(0) = 12
   \]

Thus, the derivative of the function at the given point is \( \boxed{12} \).

Would you like a more detailed explanation of any of these steps? 

### Further Questions:
1. What is the definition of a derivative?
2. How do you find the derivative of a polynomial function?
3. Can you explain the power rule for differentiation?
4. How does the chain rule apply in differentiation?
5. What is the geometric interpretation of a derivative?
6. What are the common rules for finding derivatives?
7. Can derivatives be used to find the slope of a tangent line?
8. What are higher-order derivatives?

**Tip:** When taking the derivative, always simplify the expression as much as possible before applying limit laws.

Learn how to solve the derivative problem using the limit definition. Step-by-step solution provided for the expression (3(2 + h)^2 + 2 - 14) / h. Includes detailed polynomial simplification and application of the derivative definition. Suitable for students in Grades 11-12.

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