Question

这道题的答案是什么？

高中知识，很简单

Answer 1

f(x) = (x-1)^2.(x+1)^3
f'(x) =2(x-1).(x+1)^3 +3(x-1)^2.(x+1)^2
f'(x) =0
2(x-1).(x+1)^3 +3(x-1)^2.(x+1)^2 =0
(x-1).(x+1)^2 .[ 2(x+1) +3(x-1)] =0
(x-1).(x+1)^2 .(5x-1) =0
x=1 or -1 or 1/5
f''(x)
=(x+1)^2 .(5x-1) +2(x-1).(x+1) .(5x-1) + 5(x-1).(x+1)^2
f''(1) = 16 >0 (min)
f''(-1) =0
f''(1/5) =5(-4/5)(6/5)^2 <0 (max)
max f(x) = f(1/5) = (1/5-1)^2.(1/5+1)^3 = 3456/3125
min f(x) = f(1) = 0
ans :B