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. Given \( f(x) = x^3 + x^2 f'(1) + x f''(2) + f'''(3) \). Substitute \( f'(1) = -5 \), \( f''(2) = 2 \), \( f'''(3) = 6 \).

Step 2. Calculate \( f'(x) \):  
  \( f'(x) = 3x^2 + 2x f'(1) + f''(2) \)

Step 3. Evaluate \( f'(10) \):  
  \( f'(10) = 202 \)