I'm fed up with this question from my book. I've calculated the constants to this equation but got stuck at the asymptotes and local extreme values calculations which I need to plot the graph, perhaps anyone could help me out or guide me towards the solution of calculating the asymptotes/local extreme values and then to plot the graph.

Equation:

Define the constants A,B,C so that a function which is defined by

f(x) =

(1) (6/pi) arctan(2-(x+2)²) when x < -1

(2) x + c* |x| - 1 when -1 ≥ x ≥ 1

(3) (1/Ax+B) + 4 when x > 1 och Ax + B ≠ 0

is continuous at x = -1 and differentiable in x = 1

_______________

I calculated the constants, A,B,C to:

A = -18

B = 16

C = 7/2

Any help is appreciated,

Thanks, Michael.