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Calculus and Beyond Homework Help
How can I determine the potential extrema on a function with a discontinuity?
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[QUOTE="tnich, post: 5996861, member: 639870"] First, I am a little confused. In your original problem statement you said ##y = |sinx(x)| + (1/x)##, but the problem you have actually been working on is ##y = |sin(x)| + (1/x)##. So which is it? A couple of suggestions: When you have an absolute in an equation, it can be helpful to consider each case separately. So in this problem for example, you could rewrite the function ##y = |sin(x)| + (1/x)## as ##y = \begin{cases} sin(x) + (1/x) & \text{if } -2π \leq x < -π\text{ or }0 \leq x < π\\ -sin(x) + (1/x) & \text{if } -π \leq x < 0\text{ or }π \leq x < 2π \end{cases}## Now you can find the derivative for each case. Sketching a plot of the function and it's derivative also helps in figuring out problems like this. In answer to your question, no there is not an analytic solution to this problem. You could use a root-finding method like Newton-Raphson to find approximate solutions. [/QUOTE]
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How can I determine the potential extrema on a function with a discontinuity?
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