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Why do this problem?
It requires an understanding of how to handle functions that are defined differently on different parts of their domains and how to interpret the situation when the derivative takes different values close to point but on opposite sides of the point.
Possible approach
A short problem that can be used as a lesson starter.
Key questions
What can you say about the function when $x< 0$?
What can you say about the function when $x> 0$?
Slide
Age 16 to 18
Challenge Level 
Why do this problem?
It requires an understanding of how to handle functions that are defined differently on different parts of their domains and how to interpret the situation when the derivative takes different values close to point but on opposite sides of the point.
Possible approach
A short problem that can be used as a lesson starter.
Key questions
What can you say about the function when $x< 0$?
What can you say about the function when $x> 0$?
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Power Up
Show without recourse to any calculating aid that 7^{1/2} + 7^{1/3} + 7^{1/4} < 7 and 4^{1/2} + 4^{1/3} + 4^{1/4} > 4 . Sketch the graph of f(x) = x^{1/2} + x^{1/3} + x^{1/4} -x