Find the critical points of f(x)=x2.

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

Find the critical points of f(x)=x2.

Answer: 

x=0 is the only critical point of f(x)=x2.

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>, divide both sides by 2, and see that x=0 is the only critical point.