Calculate the area of the triangle formed by the tangent to the graph of the function f(x) = (x-6)/(x-2) at the point x = 3 with the axes of the coordinate system.
AAAaannndd the bot gets it wrong yet again!
f(x) = (x-6)/(x-2)
f'(x) = 4/(x-2)^2
f'(3) = 4
f(3) = -3
so the tangent line is
y+3 = 4(x-3)
y = 4x-15
4x-y = 15
x/(15/4) - y/15 = 1
so the area = 1/2 (15/4 * 15) = 28 1/8