Finding critical points of f(x) = x^3 - 3x^2 + 3

[njm1]

Suppose that [FONT=MathJax_Math]f [FONT=MathJax_Main]([/FONT][FONT=MathJax_Math]x[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main] = [/FONT][FONT=MathJax_Math]x[/FONT]^{[FONT=MathJax_Main]3[/FONT]}[FONT=MathJax_Main] −[/FONT][FONT=MathJax_Main] 3[/FONT][FONT=MathJax_Math]x[/FONT]^{[FONT=MathJax_Main]2[/FONT]}[FONT=MathJax_Main] + [/FONT][FONT=MathJax_Main]3[/FONT][/FONT]. (a) List all the critical points of [FONT=MathJax_Math]f.[/FONT]

 

[Deleted member 4993]

Suppose that [FONT=MathJax_Math]f[FONT=MathJax_Main]([/FONT][FONT=MathJax_Math]x[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Math]x[/FONT][FONT=MathJax_Main]3[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]3[/FONT][FONT=MathJax_Math]x[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Main]3[/FONT][/FONT].(a) List all the critical points of [FONT=MathJax_Math]f.[/FONT]

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[stapel]

Suppose that [FONT=MathJax_Math]f [FONT=MathJax_Main]([/FONT][FONT=MathJax_Math]x[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main] = [/FONT][FONT=MathJax_Math]x[/FONT]^{[FONT=MathJax_Main]3[/FONT]}[FONT=MathJax_Main] −[/FONT][FONT=MathJax_Main] 3[/FONT][FONT=MathJax_Math]x[/FONT]^{[FONT=MathJax_Main]2[/FONT]}[FONT=MathJax_Main] + [/FONT][FONT=MathJax_Main]3[/FONT][/FONT]. (a) List all the critical points of [FONT=MathJax_Math]f.[/FONT]

What is the first step for finding critical points? What did you get as your result for this first step?

When you set the first step equal to zero (which is the second step) and solved, what did you get?

Please be complete. Thank you!