6. The twice-differentiable function $f$ is defined for all real numbers and satisfies the following conditions: $$f ( 0 ) = 2 , f ^ { \prime } ( 0 ) = - 4 , \text { and } f ^ { \prime \prime } ( 0 ) = 3$$ (a) The function $g$ is given by $g ( x ) = e ^ { a x } + f ( x )$ for all real numbers, where $a$ is a constant. Find $g ^ { \prime } ( 0 )$ and $g ^ { \prime \prime } ( 0 )$ in terms of $a$. Show the work that leads to your answers. (b) The function $h$ is given by $h ( x ) = \cos ( k x ) f ( x )$ for all real numbers, where $k$ is a constant. Find $h ^ { \prime } ( x )$ and write an equation for the line tangent to the graph of $h$ at $x = 0$.