Question

高一数学题求解！十分感谢

高一数学题求解！十分感谢如图，十分感谢解答！

Answer 1

y = 3^x/[9^x +3^(x+1) +2 ]
let
u=3^x
y = 3^x/[9^x +3^(x+1) +2 ]
= u/( u^2 +3u +2)
dy/du
= [( u^2 +3u +2)- u(2u+3)]/( u^2 +3u +2)^2
= ( -u^2 +2)/( u^2 +3u +2)^2
dy/du =0
u^2-2=0
u=√2 or -√2(rej)
dy/du| u=√2+ <0 , dy/du| u=√2- >0
u=√2 (max)
max y
= y(√2)
= √2/( 2 +3√2 +2)
= √2/( 4 +3√2 )
=√2( 3√2 -4 )/2
=(6 -4√2 )/2
=3 -2√2
x->-∞ , y->0
x->+∞ , y->0
值域=(0, 3-2√2 ]