1、V=(4/3)πr³
dV/dt = 4πr²dr/dt [1]
t=120s,V=5×120=600 (cm³)
600=(4/3)πr³,r=(450/π)^(⅓)
代入[1]得：
dr/dt=(dV/dt)/4πr²
=5/4πr²
=5/[4π(450/π)^(⅔)]
=0.0145 (cm/s)
2、2x²+5xp+50p²=24800
4xdx/dt+5pdx/dt+5xdp/dt+100pdp/dt=0
dx/dt=-2(5x+100p)/(4x+5p)
when p=2
2x²+100x-4800=0
x²+50x-2400=0
x₁= 30,x₂= -80(Reject)
∴dy/dt=-2(150+2000)/(120+100)=215/11=19.55 (unit/month)