Is #f(x)=(x^2+2x-6)/(2x+1)# increasing or decreasing at #x=0#?

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Answer 1 · 2017-01-19T03:30:01

#uarr#. Look for x = o, on the graph that is a hyperbola, with asynptotes #y =x/2+3/4 and 2x+1=0#.

By actual division,

#f=x/2+3/4-(27/4)/(2x+1)# and

#f'=1/2+(27/2)/(2x+1)^2=1/2+27/8=31/8>0#, at x = 0.

So, f #uarr#, at # (0, -6)#.

See the graph.

Note that the graph is a hyperbola, with asynptotes

#y =x/2+3/4 and 2x+1=0#. These meet at the

center #(-1/2, 1/2)#

graph{(y(2x+1)-x^2-2x+6)(x^2+(y+6)^2-.1)=0 [-20, 20, -10, 10]}