# Calculate asymptotes and local extreme values

• Nov 22nd 2012, 03:53 AM
Michael1
Calculate asymptotes and local extreme values
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.
• Nov 22nd 2012, 05:07 AM
prasum
Re: Calculate asymptotes and local extreme values
use the maxima-minima concept
for maxima differentiate for interval(-1,1) the value of the function of x
also check for global maxima and minima

for asymptotes
horizontal asymptote can be calculated as
lt(y tends to infinity)
=b
lt(x tends to a)=infinity
vertical asymptote at x=a
this can be found by seeing what the function is in it intervals