This problem will focus on the function:

f(x) =e^{(x2)2/(2 (122))}

which is defined for all values ofx.

(a)f ' (x)=

(b) The solution to the equationf ' (x)=0isx= .

(c)f ''(x)=

(d) The solutions to the equationf '' (x)=0arex= (smallest x value) andx= (largest x value).

(e)lim

x

f(x)

=.

(f)lim

x

f(x)

=.

(g) The maximum value off(x)on the domain of all real numbers occurs at x=.

(h) The maximum value off ' (x)on the domain of all real numbers occurs at x=.

(i) The minimum value off ' (x)on the domain of all real numbers occurs at x=