Question

Let \( f(x) = x^3 + x^2 f'(1) + x f''(2) + f'''(3) \), \( x \in \mathbb{R} \). Then \( f'(10) \) is equal to ______.

Answer 1

Correct Answer: 202

Step 1. The function is defined as \( f(x) = x^3 + x^2 f'(1) + x f''(2) + f'''(3) \). The provided values are \( f'(1) = -5 \), \( f''(2) = 2 \), and \( f'''(3) = 6 \).

Step 2. The derivative \( f'(x) \) is calculated as:
  \( f'(x) = 3x^2 + 2x f'(1) + f''(2) \)

Step 3. The value of \( f'(10) \) is determined to be:  
  \( f'(10) = 202 \)