The function f(x) = x + x has - Vidyadip

MCQ

The function $f(x) = x + \sin x$ has

A
A minimum but no maximum
B
A maximum but no minimum
✓
Neither maximum nor minimum
D
Both maximum and minimum

✓

Answer

Correct option: C.

Neither maximum nor minimum

c
(c) $ f(x) = x + \sin x$ ==> $f'(x) = 1 + \cos x$

Now $f'(x) = 0 \Rightarrow 1 + \cos x = 0 \Rightarrow \cos x = - 1 \Rightarrow x = \pi $

Now $f''(x) = - \sin x$,$f''(\pi ) = 0$,,

$f'''(\pi ) = 1 \ne 0$

$\therefore$ Neither maximum nor minimum.

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