First we have to find the tangent line: y - y o = f ` ( x o ) * ( x - x o ) f ` ( x ) = 10 x y - 80 = 40 ( x - 4 ) y = 40 x - 160 + 80 y = 40 x - 80 There are 2 parts of this region: A = A = 40/3 + 320/3 - 320 + 320 - 40/3 + 80 - 160 = 320/3 - 240/3 = 80/3