The point $P(0,4)$ lies on the curve $y=2\sqrt[\phantom{2}]{x4}.$ If $Q$ is the point $(x,2\sqrt[\phantom{2}]{x4}),$ use your calculator to find the slope $m_N$ of the secant line $PQ($correct to six decimal places$)$ for the following values of $x.(8$ points$)$

$\backslash$table$[[x,0\mathrm{.}1,0\mathrm{.}01,0\mathrm{.}001,0\mathrm{.}0001,,-0\mathrm{.}0001,-0\mathrm{.}001,-0\mathrm{.}01,-0\mathrm{.}1],[m_{re},,,,,,,,,]]$

Using the results from number $1,$ guess the value of the slope $m$ of the tangent line to the curve at $P(0,4).(1$ poin?$)$

$m$; $q,$

Using the slope from number $2,$ find the equation of the tangent line to the curve at $P(0,4).$

Please draw a box around your answer. $(1$ point$)$