Question

Let f(x) = $\{\begin{array}{c}1+sinx,x<0\\ x^2-x+1,x\ge 0\end{array}$. Then

• 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 1

The correct option is A f has a local maximum at x = 0

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