9514 1404 393
Answer:
Step-by-step explanation:
Each tangent line will be of the form ...
y = -6x + b
where b = f(x1) +6·x1 for the points f'(x1) = -6.
Taking the derivative, we get ...
f'(x) = ((x -5)(1) -(x+1)(1))/(x -5)^2 = -6/(x -5)^2
This will have a value of -6 when |x-5| = 1, or x=4 and x=6.
So, the lines are ...
at x=4
y = -6x + (f(4) +6·4) = -6x +(5/-1)+24
y = -6x +19
at x=6
y = -6 +(f(6) +6·6) = -6x +(7/1)+36
y = -6x +43
