Find the critical points of f(x)=x3.

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Lesson Parent: 
Geometry of Functions VI: Critical Points
Problem: 

Find the critical points of f(x)=x3.

Answer: 

x=0 is the only critical point of f(x)=x3.

SAMPLE SOLUTION

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Solution: 

Critical points are where either <Sign in to see all the formulas> or <Sign in to see all the formulas> does not exist. We know that the derivative is <Sign in to see all the formulas> exists and is <Sign in to see all the formulas>. We now set <Sign in to see all the formulas> and easily see that

<Sign in to see all the formulas>

Note that while x=0 is a critical point of <Sign in to see all the formulas>, it is not a maximum or minimum.