f(x)=1/3x^3+x^2-ax.若a=3,求函数f(x)的单调区间

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f(x)=1/3x^3+x^2-ax.若a=3,求函数f(x)的单调区间
f(x)=1/3x^3+x^2-ax.若a=3,求函数f(x)的单调区间

f(x)=1/3x^3+x^2-ax.若a=3,求函数f(x)的单调区间
f(x)=(1/3)x^3+x^2-3x,令f'(x)=x^2+2x-3=(x+3)(x-1)

f(x)=1/3x^3+x^2-ax
f'(x) = x^2+2x-a = (x+1)^2+1-a
当a≤1时,
f'(x)≥0,f(x)在R上单调增
即单调增区间(-∞,+∞)
当a>1时,
f'(x) = x^2+2x-a = (x+1)^2-(a-1) = {x+1+√(a-1)}{x+1-√(a-1)}
单调增区间(-∞,-1-√(a...

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f(x)=1/3x^3+x^2-ax
f'(x) = x^2+2x-a = (x+1)^2+1-a
当a≤1时,
f'(x)≥0,f(x)在R上单调增
即单调增区间(-∞,+∞)
当a>1时,
f'(x) = x^2+2x-a = (x+1)^2-(a-1) = {x+1+√(a-1)}{x+1-√(a-1)}
单调增区间(-∞,-1-√(a-1))和(-1+√(a-1),+∞)
单调减区间(-1-√(a-1),-1+√(a-1) )

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