To find out extrema, use theorem.

\ \ If f " (x) > 0 (positive) ------> minimum point. \ \ \ \ If f " (x) < 0 (negative) ------> maximum point.

f^,(x) = 8x³ - 8x = 8x(x² - 1) = 0.

The key numbers are x = 0 and x = ± 1.

So, lets plug each critical point in f " (x) = 24x² - 8. \ \ \ \ If x = - 1 then f " (- 1) = 24(- 1)² - 8 = 24 - 8 = 16 > 0 (positive), therefore local minimum point. \ \ \ \ If x = 0 then f " (0) = 24(0)² - 8 = - 8 < 0 (negative), therefore local maximum point.