Find the tangent line(s) to f(x) = (x + 1)/(x − 5)
with slope m = −6

9514 1404 393

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

right

step-by-step explanation:

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!