一道英文数学题(微积分)The dimensions of a rectangle are changing in such a way that the area remains 24 in^2.At what rate is the perimeter changing at the instant when one side is 6 in,long and is increasing at the rate of 0.3 inch per minute?
问题描述：
一道英文数学题(微积分)
The dimensions of a rectangle are changing in such a way that the area remains 24 in^2.At what rate is the perimeter changing at the instant when one side is 6 in,long and is increasing at the rate of 0.3 inch per minute?
答
bu hui
答
设周长为y，边长为x，则y=2(x+24/x)，dy/dx=2-48/x^2，当x=6，dy/dx=2/3
dx/dt=0.3，那么dy/dt=dy/dx*dx/dt=2/3*0.3=0.2，故周长的变化率为0.2inch per minute
答
Let l denote the perimeter,a one side
(l-2a)/2*a=24,that is la-2a^2=48
differentiate (l-2a)/2*a=24 respect to the time t
a*dl/dt+l*da/dt-4a*da/dt=0
a=6,da/dt=0.3 insert we have (l=(24/6+6)*2=20)
6dl/dt+20*0.3-4*6*0.3=0
dl/dt=0.2 is the answer