Applications of Derivatives - Optimization Problems

Grade 12 Maths Higher — Applications of Derivatives - Optimization Problems: 25 practice questions with instant scoring and explanations.

1. Optimization problems involve finding:
2. To maximize/minimize a quantity, we:
3. For a rectangular box with fixed volume V, surface area is minimum when:
4. To find dimensions for minimum surface area of cylinder with fixed volume V:
5. A rectangular field has fixed perimeter P. For maximum area:
6. For optimal production cost C = f(x) where x is quantity, optimal x satisfies:
7. The revenue R = p·q where p is price and q is quantity. Maximum revenue occurs when:
8. For profit P = R - C, where R is revenue and C is cost, optimal production is where:
9. A window shape: Rectangle + Semicircle on top. For fixed perimeter, maximum area occurs when:
10. The method of Lagrange multipliers is used for:
11. For Lagrange multipliers: ∇f = λ∇g means:
12. A farmer has 100m fencing. For maximum rectangular area, length and width are:
13. To minimize distance from point to curve, the connecting line is:
14. For a function y = f(x), the least value on [a,b] is found by comparing:
15. Marginal cost is the derivative of:
16. Marginal revenue equals marginal cost when:
17. For an open box with fixed total surface area, maximum volume occurs when:
18. Newton's method for finding roots uses:
19. For a projectile, maximum height occurs when:
20. In economics, elasticity of demand E = (dQ/dP)·(P/Q) measures:
21. For a given amount of fence forming a rectangle, the maximum area is achieved when:
22. The envelope of a family of curves y = f(x,c) is found by eliminating c from:
23. For optimization with constraints, checking boundary is:
24. The envelope theorem in economics relates to:
25. A rectangle of perimeter 20 m has maximum area when: