-2
0
1
2
Correct answer is B
To find the maximum value, we can use the second derivative test where, given f(x), the second derivative < 0, makes it a maximum value.
x(x+1)2=x(x2+2x+1)=x3+2x2+x
dydx=3x2+4x+1=0
Solving, we have x=−13 or −1.
d2ydx2=6x+4
When x=−13,d2ydx2=2>0
When x=−1,d2ydx2=−2<0
At maximum value of x being -1, y=−1(−1+1)2=0
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