Comprehension: \( \quad: \) Consider the real valued function \( f: R \rightarrow R \) defined a...

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Comprehension: \( \quad: \) Consider the real valued function \( f: R \rightarrow R \) defined as \( f(x)=x^{2} e^{-x} \)
Which one of the following statement is true?
(a) \( f(x) \) has a local maximum at \( x=0 \) and a local minimum at \( x=2 \)
(b) \( f(x) \) has a local minimum at \( x=0 \) and a local maximum at \( x=2 \)
(c) \( \lim _{x \rightarrow+\infty} f(x)=1 \)
(d) \( f(x) \) is an even function
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