If `f(x)={x^2,xlt=0 2sinx ,x >0'in v e s t iga t et h e` function at `x=0` for maxima/minima

If f(x)={{:(x^2,xlt=0) , (2sinx ,x >0):}' .Investigate the function at , x=0 for maxima/minima

If f(x) = {{:(x^(2),x le 0),(2 sin x,x gt 0):} , investigate the function at x = 0 for maxima/minima.

Let f(x) = {{:( 2 sin x ,, x gt 0) , ( x^(2) ,, x le 0):} . Investigate the function for maxima/minima at x = 0 .

Let f(x)= {x^(3)+x^(2)+10x, xlt0 .Investigate x=0 for local -3sinx,xge0 maxima/minima.

Let f(x)= {x^(3)+x^(2)+10x, xlt0 .Investigate x=0 for local -3sinx,xge0 maxima/minima.

Let f(x)= {x^(3)+x^(2)+10x, xlt0 .Investigate x=0 for local -3sinx,xge0 maxima/minima.

Prove that the functions do not have maxima or minima: f(x) = e^(x)

Prove that the functions do not have maxima or minima: f(x) = e^(x)

Prove that the functions do not have maxima or minima: f(x) = e^(x)

f(x)={cos(pix)/2,x >0, x+a ,xlt=0 Find the values of a if x=0 is a point of maxima.