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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- Dec 11th 2010, 07:59 AMZOOZfind 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. - Dec 11th 2010, 08:41 AMSoroban
Hello, ZOOZ!

Quote:

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

I did some simplifying first . . .

$\displaystyle \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} $

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

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

. . But $\displaystyle |\csc2x| \:\ge\:1 $ . . . $\displaystyle f'(x)$ canequal zero.*never*

Therefore, $\displaystyle \,f(x)$ hasmaximum or minimum.*no*

- Dec 12th 2010, 12:11 AMZOOZ
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.