兩道AP微積分題..

兩道AP微積分題..
1 the volume of a cone of radius r and height h is given by V=1/3πr^2 if the radius increase at a constant rate of 1/2 centimeter per second,at what rate,in cubic centimeters per second,is the volume increasing when the height is 9 centimeters and the radius is 6 centimeters?
2 the volume of a cylindrical tin can with a top and a bottom is to be 16π cubic inches.If a minimum amount of tin is to be used to construct the can,what must be the height,in inches,of the can?
麻煩用微積分方法解啦...我是幫別人問所以麻煩詳細(xì)一點(diǎn) 感激不盡！

英語人氣：421 ℃時(shí)間：2020-06-05 14:45:55

優(yōu)質(zhì)解答

1) V = (1/3)πr^2 h
如果高度不變,只是半徑增加,那么方程兩邊對時(shí)間求導(dǎo)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
限制條件：V = π r^2 h = 16π
=> h = 16/r^2 代入面積表達(dá)式,
A = 2π r^2 + 2π 16/r
對r求導(dǎo),并令A(yù)' = 0,
2r - 16/r^2 = 0
r = 2 inches
h = 16/r^2 = 4 inches
美國大學(xué)理事部認(rèn)證AP微積分AB和微積分BC教師

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兩道AP微積分題..

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