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1. Critical points: $$x=5$$ (local max), $$x=4.5$$ (local min), $$x=5$$ (local max), $$x=7$$ (local min), $$x=9.5$$ (local max), $$x=10$$ (local min). Global max at $$x=13.$$ Global min at $$x=7.$$
2. Critical points: $$x=2$$ (local min), $$x=3$$ (neither), $$x=5$$ (local max), $$x=8$$ (local min), $$x=11$$ (local max). Global max at $$x=0$$ and $$x=5.$$ Global min at $$x=8.$$
3. Critical point at $$x=-4$$ (local minimum).
4. Critical point at $$x=3$$ (local minimum).
5. Critical points at $$x = 0$$ (local maximum) and $$x=4$$ (local maximum).
6. Critical points at $$x=1$$ (local maximum) and $$x=7/3$$ (local minimum).
7. Critical point at $$x=3$$ (local minimum).
8. Critical points at $$x=-4$$ (local minimum) and $$x=4$$ (local maximum).
9. Critical point at $$x=3$$ (global minimum). No global maximum.
10. Critical point at $$x=0$$. No global minimum or global maximum.
11. Critical points at $$x=\pm 1$$. No global minimum or global maximum.
12. Critical point at $$x=0$$ (global maximum). No global minimum.
13. Critical point at $$x=3$$ (global minimum). Global maximum at $$x=-2$$.
14. Critical point at $$x=0$$. Global maximum at $$x=-2$$. Global minimum at $$x=1$$.
15. Critical points at $$x = -1$$ (global maximum) and $$x=1$$ (global minimum). There is another global minimum at $$x=-2.$$
16. Critical point at $$x=0$$. Global maximum at $$x=1$$. Global minimum at $$x=2.$$
17. a) local minimum. b) nothing. c) local maximum. d) nothing.
1. $$x=0$$ is a local maximum, $$x=5$$ is a local minimum.
2. $$x=-1$$ is a local maximum, $$x=3$$ is a local minimum.
3. $$x=\pm 2$$ are local minima, $$x=0$$ is a local maximum.