f(x)=(x+1)⅓(2x+5)3.
f'(x)=⅓(x+1)-⅔(2x+5)3+6(x+1)⅓(2x+5)2=0 at critical points.
Multiply through by 3(x+1)⅔:
(2x+5)3+18(x+1)(2x+5)2=0,
(2x+5)2(2x+5+18x+18)=0,
(2x+5)2(20x+23)=0, so x=-2.5 or -23/20=-1.15. These are the critical numbers.
f(-2.5)=0; f(-1.15)=(∛-0.15)(2.7)3=-10.4582 approx.
(The point (-2.5,0) is a point of inflection (neither max or min), while (-1.15,-10.4582) is a minimum.)