Question

Graph the following function. Find and state the domain, intercepts, asymptotes, intervals of increase and decrease, local extrema, concavity, and inflections points.
F(x)=(x+1)/(square root(x^2+1))

I got so far...
Domain: (-infinity, infinity)
Intercepts: (0,1)and(-1,0)
Asymptotes: y=O and I don't know how to get Vertiical asymptotes?
Intervals: I can't figure out how to get f prime ?


Are these right so far?
And can someone show me how to do asymptotes, intervals increase/decrease, local extrema, concavity, and inflection points?

Answer 1

so far so good

for vertical asymptotes, the denominator has to be zero (and the numerator not)
since √(x^2 + 1) can never be zero, there are no vertical asymptotes

for local extrema, take the first derivative and set it equal to zero, solving for x
sub that x back into the original equation to find the max/min.

for concavity and points of inflection, you will need the second derivative.
if y ' ' = 0 , you will have a point of inflection
if y ' ' > 0, the curve is concave upwards
if y ' ' < 0 , the curve is concave dowards for those x's