Maxima and Minima

Grade 12 Maths — Maxima and Minima: 25 practice questions with instant scoring and explanations.

1. A local maximum of f at x = c means:
2. The Second Derivative Test states: If f'(c) = 0 and f''(c) > 0, then x = c is a:
3. If f'(c) = 0 and f''(c) < 0, then x = c is a:
4. An absolute (global) maximum of f on [a, b] is the:
5. For f(x) = x² − 4x + 3, the minimum occurs at:
6. The value of the minimum of f(x) = x² − 4x + 3 is:
7. For f(x) = −x² + 6x − 5, the maximum value is:
8. To find absolute extrema on [a, b], we check:
9. If f(x) = x³ − 3x² on [−1, 2], the absolute maximum is:
10. For f(x) = x⁴ − 2x², the local extrema occur at:
11. At x = 0, f(x) = x⁴ − 2x² has a:
12. An inflection point occurs where:
13. For f(x) = sin(x) on [0, 2π], the absolute maximum is:
14. The Extreme Value Theorem states that a continuous function on [a, b]:
15. For a quadratic f(x) = ax² + bx + c with a > 0, the vertex is a:
16. The critical numbers of f(x) = x³ − 12x are:
17. For f(x) = x/(x² + 1), the maximum value is:
18. To maximize profit P = 100x − 2x² − 10, the optimal x is:
19. If f''(x) doesn't change sign at a point where f'(x) = 0, then it's a:
20. For f(x) = e^(−x²), the maximum occurs at:
21. The function f(x) = √(x − 1) on [1, 5] has absolute minimum at:
22. For constrained optimization, we use:
23. A function f has a stationary inflection point if:
24. Question?
25. Question?