Limits and Derivatives

Let x0 be the real number such that ex0+x0=0. For a given real number , define g(x)= 3xex+3x- ex- x3(ex+1) for all real numbers x. Then which one of the following statements is TRUE?

1. For =2, x x0 | g(x)+ex0x-x0 |=0
2. For =2, x x0 | g(x)+ex0x-x0 |=1
3. For =3, x x0 | g(x)+ex0x-x0 |=0
4. For =3, x x0 | g(x)+ex0x-x0 |= 23

Let k R. If x 0+ ( ( kx)+ x+x ) 2x=e6, then the value of k is

1. 1
2. 2
3. 3
4. 4