Absolute Extrema

\(f\) has a local minimum of \(-8\) at \(x=2\)

\(f\) has no local maxima

\(f\) has an absolute minimum of \(-8\) at \(x=2\)

\(f\) has no absolute maximum

1. An absolute minimum of \(-\frac{1}{6}\) at \(x=0.5\), an absolute maximum of \(\frac{1}{6}\) at \(x=-0.5\)
2. An absolute minimum of \(\frac{3\sqrt{3}}{2}\approx 2.598\) at \(x=\sqrt{3}\), an absolute maximum of \(\frac{216}{35}\approx 6.171\) at \(x=6\) 

1. Neither an absolute maximum nor an absolute minimum
2. An absolute maximum of \(-2\) at \(x=0,\) No absolute minimum 
3. An absolute minimum of \(\frac{1}{4}\) at \(x=-6,\) No absolute maximum