The math help thread

a) derivative
you said it's straightforward and easy so I'll just give it: 2x/(x^2 + 1)
b) minimum points
This has to be when the derivative is 0, so:
2x/(x^2 + 1) = 0
2x = 0
x = 0
And the derivative changes from negative to positive at this point, which is how we know it's a minimum.
c) maximum points
Same as (b) except the derivative must change from positive to negative. There are none for this function (it goes to infinity)
d) It's increasing when the derivative > 0.
2x/(x^2 + 1) > 0
2x > 0
x > 0
e) Decreasing when derivative < 0
2x/(x^2 + 1) < 0
2x < 0
x < 0
f) second derivative is a peach but it's -2(x^2-1)/(x^2+1)^2

I gotta run so really quickly...
g) concave up when d^2 > 0
h) concave down when d^2 < 0
i) inflection points when d^2 changes sign