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In the function $y=(k-x)e^x ,$

What is the effect of $k$ on the turning point of the function? I can't see any clear pattern when I change the variable.

What are some real-life scenarios to which this relationship could be applied?

Thanks!

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    I'm just curious, it seems like one of those situations where it is applicable somehow!2011-11-06

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I take it the "turning point" is the local maximum or minimum, which, by calculus, we know is where the derivative is zero. The derivative is $(k-x-1)e^x$. That's zero when $x=k-1$. So there's the effect on the turning point; it occurs at $k-1$.

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    I mean I guess you're optimizing something, so it's showing you the x of the maximum value is equal to k-1, but can anyone think of any scenario problems where this would be applied?2011-11-05