f(x)=(1+x)^2+ln(1+x) (1)求f(x)单调区间 (2)若x ∈[1/e-1,e-1]时不等式f(x)
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f(x)=(1+x)^2+ln(1+x) (1)求f(x)单调区间 (2)若x ∈[1/e-1,e-1]时不等式f(x)
f(x)=(1+x)^2+ln(1+x) (1)求f(x)单调区间 (2)若x ∈[1/e-1,e-1]时不等式f(x)
f(x)=(1+x)^2+ln(1+x) (1)求f(x)单调区间 (2)若x ∈[1/e-1,e-1]时不等式f(x)
f'(x)=2(x+1)(x+1)' + 1/(1+x)(x+1)'=2(x+1)+1/(x+1) (定义域:x≠-1)
(1)A:若f'(x)≥0,即2(x+1)+1/(x+1)≥0,解得x>-1
B:若f'(x)≤0,即2(x+1)+1/(x+1)≤0,解得x-1,所以x ∈[1/e-1,e-1],在f(x)的单调递增区间上,
所以,f(x)≤f(e-1),故不等式f(x)
定义域:x>-1
f'(x)=2(x+1)+1/(x+1) >0
f(x)为单调递增区间为:x ∈(-1, +∞)。
不等式f(x)
f(x)=ln(1+x)/x //ln(1+x)
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