Question

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

• A. (x - a)²ⁿ⁺²
• B. b - 1 - (x+1-a)²ⁿ⁺¹
• C. b - (x - a)²ⁿ⁺²
• D. (x - a)²ⁿ⁺² - b.

Answer 1

The correct option is C

b - (x - a)²ⁿ⁺²

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.
$\therefore f\left(x\right)=b-(x-a{)}^{2n+2}(\because f^{2n+2}\left(a\right)=-ve)$
Hence (c) is the correct answer.