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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).
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