`g(t) = (t^2)/(t^2 + 3), [-1,1]` Find the absolute extrema of the function on the closed interval.
Find the critical values for t by setting the derivative equal to zero and solving for the t value(s).
` ` `2t^3+6t-2t^3=0`
Plug in the critical t value(s) and the endpoints of the closed interval into the g(t) function.
Examine the g(t) values to determine the absolute extrema.
The absolute maximum is the points are `(-1, 1/4), (1,1/4).`
The absolute minimum is the point (0, 0).