Find the maximum area of a triangle formed in the first quadrant by the x -axis, y -axis and a tangent line to the graph of f=(x+10)^-2.

Answer 1

f'(x) = -2/(x+10)^3
So, the tangent line through (h,k) on the curve is
y - 1/(h+10)^2 = -2/(h+10)^3 (x-h)

Find the intercepts of that line (a,0) and (0,b)
and the area is A = ab/2
Now find where dA/dh = 0 for maximum area