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k3k3
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Homework Statement
Let h:(0,1)→ℝ be defined by h(x)=cos([itex]\pi\\[/itex]/x). Determine the set of all x such that x has a relative extreme value at x.
Homework Equations
The Attempt at a Solution
It is common knowledge that the min and max are -1 and 1. Using intuition, it is clear by guess and check to arrive at x=1/(2n+1) gives a minimum and x=1/2n gives a maximum.
Using the first derivative test, I arrive at 1=0 which is not true. I am unsure how to interpret this answer.
Trying to solve [itex]d^{2}[/itex](cos([itex]\pi\\[/itex]/x))/d[itex]x^{2}[/itex]=0 is proving to be a real challenge.
I am only concerned about this since my professor wants me to show my work, so I do not think saying I guessed and checked will be acceptable.