The interval in which the function $f (x) = x e^{x}$ is strictly increasing is

(-∞,-1)

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(-1,-∞,)

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(-2, ∞)

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(-∞, -2)

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Solution

The correct option is B
(-1,-∞,)

$f (x) = x e^{x} \Rightarrow f^{'} (x) = (x + 1) e^{x} f^{'} (x) > 0 \Rightarrow (x + 1) e^{x} > 0 \Rightarrow x + 1 > 0 \Rightarrow x > - 1 \Rightarrow x ϵ (- 1, \infty)$

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