求极值和单调区间求函数f(x)＝x3+2x2-7x+1(x后的数字为次方)的极值和单调增区间

Question

求极值和单调区间
求函数f(x)＝x3+2x2-7x+1(x后的数字为次方)的极值和单调增区间

Answer 1

f'(x)＝3x^2＋4x－7＝(x-1)(3x+7).令f'(x)＝0得驻点x＝1,-7/3
x＜-7/3时,f'(x)＞0,函数f(x)在(-∞,-7/3]上单调增加
-7/3＜x＜1时,f'(x)＜0,函数f(x)在[-7/3,1]上单调减少
x＞1时,f'(x)＞0,函数f(x)在[1,+∞)上单调增加
所以,f(x)在x＝-7/3处取得极大值f(-7/3)＝419/27,在x＝1处取得极小值f(1)＝-3