This problem will focus $on$ the function:

$f(x)=e^{-\frac{(x-5{)}^2}{2(8^2)}}$

which $is$ defined for all values $ofx.$

$(a)f^{\text{'}}(x)=$

$(b)$ The solution $to$ the equation $f^{\text{'}}(x)=0isx=$

$(c)f^{\text{'}\text{'}}(x)=$

$(d)$ The solutions $to$ the equation $f^{\text{'}\text{'}}(x)=0$ are $x=$

$(smallestx$ value$)$ and $x=$

$(e)\underset{x}{lim}f(x)=$

$(f)\underset{x-}{lim}f(x)=$

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

$(h)$ The maximum value $of{f}^{\text{'}}(x)on$ the domain $of$ all real numbers occurs $atx=$

$(i)$ The minimum value $of{f}^{\text{'}}(x)on$ the domain $of$ all real numbers occurs $atx=$