A function f such that f ( a ) = f ′′ ( a ) = . . . . . . f 2 n ( a ) = 0 and f has a local maximum value b at x = a, if f (x) is Options: A . &nbsp ( x − a ) 2 n + 2 B . &nbsp b − 1 − ( x + 1 − a ) 2 n + 1 C . &nbsp b − ( x − a ) 2 n + 2 D . &nbsp ( x − a ) 2 n + 2 − b .

A function f such that f(a)=f′′(a)=......f2n(a)=0 and f has

Discussion Forum : Application Of Derivatives

Question -

A function f such that $f (a) = f^{''} (a) = . . . . . . f^{2 n} (a) = 0$ and f has a local maximum value b at x = a, if f (x) is

Options:

A .

(x - a)^{2 n + 2}

B .

b - 1 - (x + 1 - a)^{2 n + 1}

C .

b - (x - a)^{2 n + 2}

D .

(x - a)^{2 n + 2} - b .

Answer: Option C
:
C

For local maximum or local minimum odd derivative must be equal to zero.
For local maxima, even derivative must be negative.
Since maximum value at x = a is b.
$∴ f (x) = b - (x - a)^{2 n + 2} (∵ f^{2 n + 2} (a) = - v e)$
Hence (c) is the correct answer.

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Discussion Forum : Application Of Derivatives

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