Prove that $f(x)=x$ has no concavity.

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Lesson Parent: 
Geometry of Functions IX: Concavity
Problem: 

Prove that $f(x)=x$ has no concavity.

Answer: 

It is true that $f(x)=x$ has no concavity.

SAMPLE SOLUTION

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Solution: 

The derivative of <Sign in to see all the formulas> is <Sign in to see all the formulas>. Its derivative is constant and never changes. Therefore the function cannot be either concave up or concave down.