Increasing/Decreasing Functions, Maxima & Minima

Grade 12 Maths Higher — Increasing/Decreasing Functions, Maxima & Minima: 25 practice questions with instant scoring and explanations.

1. A function f is increasing on interval I if:
2. A function f is decreasing on interval I if:
3. A critical point of f(x) is where:
4. For f(x) = x³ - 3x, the critical points are:
5. First Derivative Test: If f'(x) changes from + to - at c, then c is:
6. If f'(x) changes from - to + at c, then c is:
7. Second Derivative Test: If f'(c) = 0 and f''(c) < 0, then c is:
8. If f'(c) = 0 and f''(c) > 0, then c is:
9. For f(x) = (x-1)³, at x = 1:
10. Absolute maximum of f on [a,b] occurs at:
11. For f(x) = x² - 4x + 3 on [0, 3], the maximum value is:
12. The minimum value of f(x) = x² - 4x + 3 on [0, 3] is:
13. For f(x) = 1/x on (-∞, 0) ∪ (0, ∞):
14. A local extremum point must be a:
15. The Second Derivative Test is inconclusive when:
16. For f(x) = e^(-x²), the maximum occurs at:
17. A function with f'(x) = 0 nowhere on interval I is:
18. For f(x) = |x - 2|, critical/non-differentiable point is at:
19. If f is continuous on [a,b] and has no critical points, then extrema occur at:
20. The Extreme Value Theorem requires f to be:
21. For f(x) = x³, f'(x) = 3x²: At x = 0:
22. Monotonicity test: If f'(x) > 0, then f is:
23. A function can have at most ___ local extrema between consecutive critical points:
24. If f'(x) > 0 for all x, then f has:
25. Review question for Increasing/Decreasing Functions, Maxima & Minima