Given that f'(x)=[(8cos(x)/(x(adsbygoogle = window.adsbygoogle || []).push({}); ^{2})-(⅛)], find the number of relative maxima and minima on the interval (1,10). Finding maxima and minima analytically wasn't fruitful for me, so instead I used a bit of handwaving. First I argued, using the intermediate value theorem, since f'(1)>f'(10), there exists at least one maximum or minimum. Then I said, well, the derivative is approximately equal to 8cos(x)/x^{2}and since cos(x) has 2 minima and one maximum on the interval (1,10), then f(x) must have 2 minima and one maximum on that same interval.

Is there way to solve this without that handwaving?

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# I Critical points for difficult function

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