Question

设函数F(X)=X^3+X^2-X,求函数单调区间和极值

Answer 1

F(X)=X^3+X^2-X
F ‘ (X) = 3X^2+2X-1 = (X+1)(3X-1)
X∈(-∞,-1)时,单调增；
X∈(-1,1/3)时,单调减；
X∈(1/3,+∞)时,单调增.
极大值f(-1) = -1+1+1=1
极小值f(1/3) = 1/27+1/9-1/3=-5/27