Consider the function $y=g(x) = -x^{2}+3x+6$.

(a) Use the limit definition to compute a formula for $y=g'(x)$.
$y =$

(b) Determine the slope of the tangent line to $y=g(x)$ at the value $x=2$.
slope =

(c) Compute $g(2)$.
$g(2) =$

(d) The equation for the tangent line to $y=g(x)$ at the point $(2,g(2))$, written in point-slope form, is
$y -$ $=$ $(x -$ $)$
Fill in the blanks with the appropriate numbers.