Application of Derivatives
Maxima and Minima
Premium Question
Grade 12
Question:
If $f(x) = x^3 + ax^2 + bx + c$ has a local maximum at $x = -1$ and a local minimum at $x = 3$, then $a + b$ equals:
(1) $-12$
(2) $-6$
(3) $6$
(4) $12$
Step-by-Step Solution
Key Concept: The critical points $-1$ and $3$ must be the roots of $f'(x) = 3x^2 + 2ax + b = 0$ — use the sum and product of roots to set up two equations in $a$ and $b$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)