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Question: Detecting increasing / decreasing functions

Question:Detecting increasing / decreasing functions

Doug Meade 3073 Maple
April 03 2007
0
I know I have done this before, but I'm not having any luck today. I am using Maple 10. I want to check if a user-entered function is positive for values in a bounded or unbounded interval. I do not want to do too much that is fancy, just functions that are likely to show up in the integral test for convergence of a series. Specific question: How can I get Maple to report that 1/sqrt(k) is decreasing for all k>1? I have tried working with both sqrt and surd, and with various assumptions. But, nothing gives a useful result. 
f := 1/sqrt(k);       # no information
solve( diff(f,k)
g := 1/surd(k,2);     # no information
solve( diff(g,k)
h := exp(-k);         # works fine
solve( diff(h,k)
s := (k-2)*exp(-k);   # works fine
solve( diff(s,k)
I have tried working with both sqrt and surd, and with various assumptions. But, nothing gives a useful result. No difference if I convert the derivative to a surd. Any suggestions? Thanks in advance, Doug
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