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List all local extreme points and all absolute extreme points for each of the following functions, noting carefully its domain of definition. Classify each extreme point by type.

• [math]3x^5 - 5x^3 + 7[/math]; domain: all real numbers.
• [math]4x^3 + 3x^2 - 6x + 5[/math]; domain: all real numbers.
• [math]x + \frac{a^2}x[/math]; domain: all nonzero numbers.
• [math]2x^3 - 21x^2 + 60x - 25[/math]; domain: all nonnegative real numbers.
• [math]\frac{x^2}{x-1}[/math]; domain: all real numbers except [math]1[/math].
• [math]3x^4 - 20x^3 - 36x^2 + 54[/math]; domain: all nonpositive real numbers.
• [math](x-1)^2(x+1)^3[/math]; domain: all nonnegative real numbers no greater than [math]2[/math].
• [math]2-(x+4)^\frac23[/math]; domain: all real numbers.
• [math](x-1)^2(x-4)[/math]; domain: all nonnegative real numbers.