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设函数f(x)=e^X-1-x-ax^2,若a=0,求f(x)的单调区间。
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若a=0 定义域x∈R
f(x)=e^X-1-x
f'(x)=e^(x-1)-1
令f'(x)>0 e^(x-1)-1>0 e^(x-1)>1=e^0 x-1>0 x>1
f(x)的单调递增区间为 (1,+无穷)
令f'(x)<0 e^(x-1)-1<0 e^(x-1)<1=e^0 x-1<0 x<1
f(x)的单调递减区间为 (-无穷,1)
f(x)=e^X-1-x
f'(x)=e^(x-1)-1
令f'(x)>0 e^(x-1)-1>0 e^(x-1)>1=e^0 x-1>0 x>1
f(x)的单调递增区间为 (1,+无穷)
令f'(x)<0 e^(x-1)-1<0 e^(x-1)<1=e^0 x-1<0 x<1
f(x)的单调递减区间为 (-无穷,1)
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