Let f(x) = { 1 + s i n x , x < 0 x 2 − x + 1 , x ≥ 0 . Then Options: A . &nbsp f has a local maximum at x = 0 B . &nbsp f has a local minimum at x = 0 C . &nbsp f is increasing every where D . &nbsp f is decreasing everywhere

Let f(x) = {1 + sin x, x

Question -

Let f(x) = ${\begin{matrix} 1 + s i n x, x < 0 x^{2} - x + 1, x \geq 0 \end{matrix}$ . Then

Options:

A . f has a local maximum at x = 0

B . f has a local minimum at x = 0

C . f is increasing every where

D . f is decreasing everywhere

Answer: Option A
:
A

f is continuous at ‘0’ and f' (0-) $>$ 0 and f' ( 0 +) $<$ 0 . Thus f has a local maximum at ‘0’.

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