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Discuss the extremum of f(x)={1+sinx ,x...

Discuss the extremum of `f(x)={1+sinx ,x<0x^2-x+1,xgeq0a tx=0`

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Verified by Experts

The correct Answer is:
Point of local maxima
f(0)=0
`f(x0)=underset(xrarr0)lim(x^(2)-x+1)rarr1^(-)`
as `x^(2)-x+1` is decresing for `(-oo,1//2)`
`f(0)rarrunderset(xrarr0)lim(1+sinx)rarr1^(-)`
Thus `f(0)lt and f(0) gt f(0)`
Then at x =0 f(X) is the point of maxima.
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