✔ 最佳答案
若x+y=2,x>=0,y>=0則4^x+8^y的最大最小值分別為何?
Sol
4^x+8^y
=2^(2x)+2^(3y)
=2^(2x)/3+2^(2x)/3+2^(2x)/3+2^(3y)/2+2^(3y)/2
=[2*2^(2x)+2*2^(2x)+2*2^(2x)+3*2^(3y)+3*2^(3y)]/6
=(5/6)*[2*2^(2x)+2*2^(2x)+2*2^(2x)+3*2^(3y)+3*2^(3y)]/5
>=(5/6)*[72*2^(6x+6y)]^(1/5)
=(5/6)*72^(1/5)*2^(12/5)
=(5/6)*2^(3/5)*3^(2/4)*2^(12/5)
=(5/6)*2^(3/5+12/5)*3^(2/5)
=(5/6)*8*3^(2/5)
=(20/3)*3^(2/5)……………………..(1)
f(x,y)=2^(2x)+2^(3y)
f(2.0)=2^4+2^0=17………………..(2)
f(0.2)=2^0+4^3=65………………..(3)
綜合(1),(2),(3)
(20/3)*3^(2/5)<=4^x+8^8<=65