Consider the function $f(x)=\sqrt[\phantom{2}]{x}.$

$($a$)$ Sketch $f(x)$ and the tangent at $x=1$

$f(x)=\sqrt[\phantom{2}]{x}=\sqrt[\phantom{2}]{1}=1,F(x)$

$($b$)$ Find the average rate of change in $f$ on the interval $1,x$

$($c$)$ Explain how we can find the slope of tangent line at $(1,1)$