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

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+10 x ,\ \ x<0-3sinx ,\ \ \ \ xgeq0 . Investigate x=0 for local maxima/minima.

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

Examine the continuity of the function f(x)={3x-2,xlt=0x+1,x >0"a t"x=0 Also sketch the graph of this function.

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

Examine the following functions for maxima and minima : f(x)=x^(2)e^(x) .

Iff(x)={s i^(-1)(sinx),x >0pi/2,x=0,t h e ncos^(-1)(cosx),x<0 x=0 is a point of maxima x=0 is a point of minima x=0 is a point of intersection non eoft h e s e

If f(x) = (e^(x)-e^(sinx))/(2(x sinx)) , x != 0 is continuous at x = 0, then f(0) =

Let f:R to R be defined as f(x)=e^(-x)sinx . If F:[0, 1] to R is a differentiable function such that F(x)=int_(0)^(x)f(t)dt , then the vlaue of int_(0)^(1)(F'(x)+f(x))e^(x)dx lies in the interval