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We are tasked with finding the second derivative of the function \( f(x) = 3x^5 \) at the point \( x = 3 \).

### Step 1: Find the first derivative of \( f(x) \)
The given function is:
\[
f(x) = 3x^5
\]
Differentiate \( f(x) \) with respect to \( x \):
\[
f'(x) = 15x^4
\]

### Step 2: Find the second derivative of \( f(x) \)
Now, differentiate \( f'(x) = 15x^4 \) with respect to \( x \):
\[
f''(x) = 60x^3
\]

### Step 3: Evaluate the second derivative at \( x = 3 \)
Substitute \( x = 3 \) into \( f''(x) \):
\[
f''(3) = 60(3)^3 = 60 \times 27 = 1620
\]

Thus, the second derivative of the function at \( x = 3 \) is \( 1620 \).

Let me know if you would like more details or further clarifications!

### Related questions:
1. What is the second derivative of \( f(x) = 5x^6 \) at \( x = 2 \)?
2. How do you find the third derivative of a function?
3. What is the geometric interpretation of the second derivative?
4. Can you apply this technique to any power function?
5. What are the applications of higher-order derivatives in physics?

**Tip**: When calculating higher-order derivatives, remember that each differentiation reduces the degree of the polynomial by 1.

What is the second derivative of f(x) = 3x^5 at the point x = 3?

Learn how to find the second derivative of the function f(x) = 3x^5 at x = 3. This calculus problem involves differentiating the function twice and evaluating it at a specific point, providing essential practice for high school calculus students.

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