嘉定一中AP选修课
AP Calculus BC
课程概览
Microeconomics
首页
/
Calculus BC
/
Assignment 5: Applications of Derivatives
Assignment 5: Applications of Derivatives
导数的应用
练习导数的应用：优化、曲线绘制、中值定理
✍️ 5 题
1. Find the critical numbers of f(x) = x³ - 3x + 1
A. x = ±1
B. x = 0
C. x = ±√3
D. x = 1, -3
2. Find the absolute maximum of f(x) = x² - 4x + 3 on [0, 3]
A. f(0) = 3
B. f(2) = -1
C. f(3) = 0
D. f(1) = 0
3. A farmer has 100 feet of fencing. What dimensions of a rectangle maximize the area?
A. 25 × 25 (square)
B. 50 × 50
C. 20 × 30
D. 10 × 40
4. On which interval is f(x) = x³ - 3x concave up?
A. (0, ∞)
B. (-∞, 0)
C. (-∞, -1) ∪ (1, ∞)
D. (-1, 1)
5. If f(x) is continuous on [a,b] and differentiable on (a,b), the Mean Value Theorem guarantees there exists c in (a,b) such that:
A. f'(c) = (f(b)-f(a))/(b-a)
B. f(c) = (f(a)+f(b))/2
C. f'(c) = 0
D. f(b) - f(a) = 0
提交答案
重新作答