Discuss the extremum of `f(x) = {{:(1 + sin x,x lt 0),(x^(2) - x + 1,x ge 0):}` at x = 0.

Discuss the extremum of f(x) = sin x (1 + cos x), x in (0, pi//2) .

Discuss the extremum of f(x) = x^(2) + (1)/(x^(2))

Discuss the continuity of the function f(x)={(sin x/x , if , x<0),( x+1 , if, x ge 0):}

Let f(x) = {{:(x^(3) + x^(2) + 10x, x lt 0),(-3 sin x,x ge 0):} . Investigate x = 0 for local maxima/minima.

Discuss the continuity of the function f(x)={(2 x , if , xlt0),( 0, if, 0 le x le 1),( 4 x, if , xgt1):}.

Discuss the continuity of the function f(x)=1/x,xne0