Let f be the function defined by
f\left(x\right)=\left(x+x^2\right)e^{-2x}
f(x)=(x+x 2 )e −2x
On which of the following open intervals is f increasing?
answer choices
a. \left(-\infty,\ \frac{-3-\sqrt{5}}{2}\right)\ and\ \
b. left(\frac{-3+\sqrt{5}}{2},\ \infty\right)(−[infinity], 2−3− 5
) and ( 2−3+ 5 , [infinity])\left(-\infty,\ -1\right)\ and\ \left(0,\ \infty\right)
(−[infinity], −1) and (0, [infinity])
c. \left(-\infty,\ -\frac{\sqrt{2}}{2}\right)\ and\ \left(\frac{\sqrt{2}}{2},\ \infty\right)
(−[infinity], − 22 ) and ( 22 , [infinity])
d. \left(-\frac{\sqrt{2}}{2},\ \frac{\sqrt{2}}{2}\right)(− 22 , 22 )
