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Sufficient Condition for an Extrema

Let f x = x...

Question

Let $f (x) = {(x^{2} - 1)}^{n} (x^{2} + x - 1)$ then $f (x)$ has local extremum at $x = 1$ when

n = 2

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n = 3

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n = 4

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n = 5

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Solution

The correct options are
A $n = 2$
D $n = 4$
Hence from the nth derivative test, we get a local extremum if and only if
$n ϵ 2, 4, 6..$ .
That is if 'n' is even.

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