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Given that y=x(x+1)2, calculate the maximum value...

Given that y=x(x+1)2, calculate the maximum value of y.

A.

-2

B.

0

C.

1

D.

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