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

1 Answer
Jan 19, 2017

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

Explanation:

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]}