Notes on a WebWork problem

Suppose we want to find the maximum area of a triangle formed in the first quadrant by the x-axis, the y-axis and a tangent line to the graph of (Subscript[f, a])(x)=1/(((x+a))^2). I guess the situation looks like so:

f[a_][x_] = 1/(((x+a))^2);
ℓ[a_,x0_][x_]=f[a][x0]+f[a]'[x0](x-x0)
Manipulate[
Plot[{f[a][x],ℓ[a,x0][x]},{x,0,20}, 
PlotRange -> {{0,20},{0,f[a][0]}}],
{{a,5},Range[10], SetterBar},{{x0,4.5},0,12}]

Here are some relevant computations:

xIntercept[a_,x0_] = x /. First[Solve[ℓ[a,x0][x]==0,x]]
xIntercept[a_,x0_] = Simplify[xIntercept[a,x0]]
yIntercept[a_,x0_] = Simplify[ℓ[a,x0][0]]
area[a_][x0_] = xIntercept[a,x0]*yIntercept[a,x0]/2
area[a_][x0_] = xIntercept[a,x0]*yIntercept[a,x0]/2
Simplify[area[a]'[x0]]