JEE Advance - Mathematics (1994 - No. 34)
The function defined by $$f\left( x \right) = \left( {x + 2} \right){e^{ - x}}$$
decreasing for all $$x$$
decreasing in $$\left( { - \infty , - 1} \right)$$ and increasing in $$\left( { - 1,\infty } \right)$$
increasing for all $$x$$
decreasing in $$\left( { - 1,\infty } \right)$$ and increasing in $$\left( { - \infty , - 1} \right)$$