Help with relative max and mins using derivatives...?

Question

Let f(x) = (x^2)/(x^2 + 3)

a) find f'(x), solve f'(x) = 0 and get y -coordinate also.
b) On what interval of x's is f'(x) < 0 ?
c) On what interval of x's is f'(x) > 0 ?
d) Of the points found in (a), which one is a max, which is a min.


I can do this very easily on the calculator but we are supposed to show work. Also, part a is very simple for me to do but I don't know how to "properly" show parts b and c.

thank you

Answer 1

f´(x) = 6x/(x^2+3)^2
f´(x) = 0 for x=0 y =0
sign depends on x
-----------(0)++++++++++
f(0) is min.