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**HallsofIvy** dy/dx has four factors- $\displaystyle x^2$, $\displaystyle (x+ 1)^2$, $\displaystyle (x- 2)^2$, and $\displaystyle x^2- 2x- 6$. The first three are **squared** so are never negative- the sign of the derivative is the sign of $\displaystyle x^2- 2x- 6= x^2+ 2x+ 1- 7= (x+ 1)^2- 7$ which changes sign at $\displaystyle x= -1\pm\sqrt{7}$, the -1.65 and 3.65 you give. But that means that dy/dx> 0 for x> 3.65 or x< -1.65 and is negative for x between -1.65 and 3.65. It is certainly NOT true that the derivative is negative for all x< 0.