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

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 $f'(10)$:
$f'(10) = 202$