What are the absolute extrema of #f(x) =x^4 − 8x^2 − 12 in[-3,-1]#?
Absolute extrema of a closed interval occur at the endpoints of the interval or at
That means we'll have to set the derivative equal to
So, starting with taking the derivative:
Setting it equal to
Thus the solutions are
We immediately get rid of
Finally, we evaluate these one by one to see what the absolute min and max are: