Question

Let \( f:\mathbb{R}\rightarrow \mathbb{R} \) be a function such that \( f(x)=x^{3} + x^{2}f^{\prime}(1) + x f^{\prime\prime}(2) + 6 \) for \( x \in \mathbb{R} \), then \( f(2) \) equals

• A. 30
• B. -4
• C. -2
• D. 8

Hint:

Calculus Tip:When a function's definition includes its own derivatives evaluated at specific points (like $f'(1)$ or $f''(2)$), treat those terms strictly as unknown constants, then differentiate and substitute those specific $x$-values to form a solvable system of linear equations.

Answer 1

The Correct Option is C