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Jinliang

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    calculus

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  1. I am stuck on figuring out why the following function is a increasing function when I read a paper. The function is following where where , and the independent variable x is on interval . I have plotted the function curves of f(x) with different c by the following, and found that it seems to be monotonic function. However, it is too hard to me to prove it. The first derivative of f(x) is by the following: The second derivative of f(x) is by the following:
  2. How to prove the following function is decreasing function? f(x) = (cx-c*x+x-1)/(2x-x-1), where 1<c<2, and the independent variable is on interval (0.5,1).
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