Question

两道AP微积分题..1 the volume of a cone of radius r and height h is

Answer 1

1) V = (1/3)πr^2 h

如果高度不变,只是半径增加,那么方程两边对时间求导得,

V' = (2/3)πrr' h = (2/3)π(6)(1/2)*9 = 18π cm^3/sec

2) A = 2π r^2 + 2π r h

限制条件：V = π r^2 h = 16π

=> h = 16/r^2 代入面积表达式,

A = 2π r^2 + 2π 16/r

对r求导,并令A' = 0,

2r - 16/r^2 = 0

r = 2 inches

h = 16/r^2 = 4 inches

美国大学理事部认证AP微积分AB和微积分BC教师