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Math Help - find the Local minimum or Maximum Of the Function

  1. #1
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    find the Local minimum or Maximum Of the Function

    how i find the Local minimum or Maximum?

    (there is an option that there is no Local minimum or Maximum point in this Function)

    BUT i need to show the way.

    thanks.
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  2. #2
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    Hello, ZOOZ!

    \text{Find the local minimum or maximum (if any): }\;f(x) \:=\:\cot x - \tan x

    I did some simplifying first . . .

    \displaystyle f(x) \;=\; \cot x - \tan x \;=\;\frac{\cos x}{\sin x} - \frac{\sin x}{\cos x} \;=\;\frac{\cos^2\!x - \sin^2\!x}{\sin x\cos x}

    . . . . \displaystyle =\;\frac{\cos2x}{\frac{1}{2}\sin2x} \;=\;2\cot2x


    Set the derivative equal to zero: . f'(x) \;=\;-4\csc^2\!2x \;=\;0

    . . But |\csc2x| \:\ge\:1 . . . f'(x) can never equal zero.


    Therefore, \,f(x) has no maximum or minimum.

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  3. #3
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    i think you mistake with Absolute minimum and Absolute maximum .

    BUT to find Local minimum or Maximum we not must that the derivative will equal to zero.

    but still thanks about your answer.
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