Let \( f(x)=x^{n+1}+a \cdot x^{n} \), where \( a \) is a positive real number. Then, \( x=0 \) i...

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Let \( f(x)=x^{n+1}+a \cdot x^{n} \), where \( a \) is a positive real number. Then, \( x=0 \) is a point of
(a) local minimum for any integer \( n \)
(b) local maximum for any integer \( n \)
(c) local minimum if \( n \) is an even integer
(d) local minimum if \( n \) is an odd integer
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