Thinking $(16$ marks$)$

$10.$ Determine the equation of the tangent to $y=x^2-4\sqrt[\phantom{2}]{x}$ at $x=4.[5$ marks$]$

$11.$ The line $8x-y-8=0$ is tangent to the graph of $f(x)=(x+k)(x^2-1)$ at the point $(1,0).$ Find the value of $k.[5$ marks$]$