SOLUTION: Determine the coordinates of the turning points and conclude the maximum turning point of the equation y= (x^2 -3)(x+3)

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Question 986686: Determine the coordinates of the turning points and conclude the maximum turning point of the equation y= (x^2 -3)(x+3)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
y=%28x%5E2-3%29%28x%2B3%29
y=x%5E3%2B3x%5E2-3x-9
Taking the derivative,
dy%2Fdx=3x%5E2%2B6x-3=3%28x%5E2-2x-1%29
Setting it equal to zero to solve for the extrema,
x%5E2-2x-1=0
%28x%5E2-2x%2B1%29-1=1
%28x-1%29%5E2=2
x-1=0+%2B-+sqrt%282%29
x=1+%2B-+sqrt%282%29
So when x=1-sqrt%282%29,y=4+%2B+8sqrt%282%29
and when x=1%2Bsqrt%282%29,y=4+-+8sqrt%282%29
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