To find critical points you first need to find derivative of your function:
f'(x) = 3x^2 + 8x
3x^2 + 8x = 0
x(3x+8) = 0
x=0 and x = -8/3
if x = 0 then y = -3
if x = -8/3 then y = 175/27 = 6.48
from the graph we see that relative maxima is at x = -8/3, and relative minima at x = 0
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