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Differentiate following functions.
g ( x ) = 3sec ( x ) -10 cot ( x )
Solution : There actually isn't a whole lot to this problem. We'll just differentiate each term by using the formulas from above.
g′ ( x ) =3sec ( x ) tan ( x ) -10 (- csc2 ( x ))
=3sec (x ) tan ( x ) +10 csc2 (x )
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First, see that the right hand side of equation (2) is a polynomial and thus continuous. This implies that this can only change sign if this firstly goes by zero. Therefore, if the
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