Question

求极值，一道题

求极值，一道题就要第一道

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Answer 1

(1)
f(x)=6x^2-x-2
=6(x- 1/3)^2 - 8/3
min f(x) = f(1/3) = -8/3
(2)
f(x)=x^3-27x
f'(x)= 3x^2 -27
f'(x)=0
3x^2 -27=0
x=3 or -3
f''(x) =6x
f''(3)=18 >0 (min)
f''(-3)=-18<0 (max)
max f(x) = f(-3)= 108
min f(x)= f(3) =0
(3)
f(x)=3x-x^3
f'(x)= 3 -3x^2
f'(x) =0
3 -3x^2=0
x=1 or -1
f''(x) =-6x
f''(1) =-6 <0 (max)
f''(-1)=6>0 (min)
max f(x) = f(1) =2
min f(x)=f(-1)=-2

Answer 2

请采纳谢谢

追问

这个不用画图吗

追答

不用啊，化成顶点式就可以了