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Integral Calculus> options x = a is a point of minimum x = a...

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options

x = a is a point of minimum

x = a is a point of maximum

x = a is not a point of maximum or minimum

None of these

Aditya Kartikeya , 10 Years ago

Grade 10

1 Answers

Jitender Singh

Last Activity: 10 Years ago

Ans:
Hello Student,
Please find answer to your question below

$f'(x) = (x-a)^{2n}(x-b)^{2m+1}$
$f''(x) = (x-a)^{2n}[(2m+1)(x-b)^{2m}] + (x-b)^{2m+1}[2n(x-a)^{2n-1}]$ Since
2n-1 > 0
$f''(a) = (a-a)^{2n}[(2m+1)(a-b)^{2m}] + (a-b)^{2m+1}[2n(a-a)^{2n-1}]$
$f''(a) = (0)^{2n}[(2m+1)(a-b)^{2m}] + (a-b)^{2m+1}[2n(0)^{2n-1}]$
$f''(a) = 0+0$
$f''(a) = 0$
So x = a is neither maximum nor minimum.

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