The point $P(4,6)$ lies $on$ the curve $y=\sqrt[\phantom{2}]{x}+4.IfQis$ the point $(x,\sqrt[\phantom{2}]{x}+4),$ find the

slope $of$ the secant line $PQ$ for the following values $ofx.$

Enter the slopes $of$ the secant lines accurate $toat$ least $4$ decimal places.

$Ifx=4\mathrm{.}1,$ the slope $ofPQis$:

and $ifx=4\mathrm{.}01,$ the slope $ofPQis$:

and $ifx=3\mathrm{.}9,$ the slope $ofPQis$:

and $ifx=3\mathrm{.}99,$ the slope $ofPQis$:

Based $on$ the above results, guess the slope $of$ the tangent line $to$ the curve $atP(4,6).(number$ not what type $of$ slope $itis)$