Consider the function $f(x)=4e^x-8$

$($a$)$ Find the points, if any, at which the graph of each function $f$ has a horizontal tangent line. $($If an answer does not exist, enter DNE.$)$

$(x,y)=$

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$($b$)$ Find an equation for each horizontal tangent line. $($If an answer does not exist, enter DNE. Enter your answers as a comma$-$separated list of equations.$)$

$$

$($c$)$ Solve the inequality $f^{\text{'}}(x)>0.($Enter your answer using interval notation. If an answer does not exist, enter DNE.$)$

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$($d$)$ Solve the inequality Enter your answer using interval notation. If an answer does not exist, enter DNE.$)$

$($e$)$ Graph $f$ and any horizontal lines found in $($b$)$ on the same set of axes. $($A aranhina calculator ic rernmmonion $)$