find-max-and-min-value-of-function-f-x-5-3cos-x-4sin-x-

Question Number 88042 by jagoll last updated on 08/Apr/20

find \max and \min value of

function f (x) = \frac{5}{- 3 \cos x - 4 \sin x}

Answered by mr W last updated on 08/Apr/20

f (x) = \frac{5}{- 3 \cos x - 4 \sin x}

= \frac{1}{- (\frac{3}{5} \cos x + \frac{4}{5} \sin x)}

= \frac{1}{- (\cos α \cos x + \sin α \sin x)} w i t h α = \tan^{- 1} \frac{4}{3}

= \frac{1}{- \cos (x - α)}

\Rightarrow m a x . f (x) \to + \infty w h e n \cos (x - α) \to 0^{-}

\Rightarrow m i n . f (x) \to - \infty w h e n \cos (x - α) \to 0^{-}

\Rightarrow l o c a l m a x . f (x) = - 1 w h e n \cos (x - α) = 1

\Rightarrow l o c a l m i n . f (x) = 1 w h e n \cos (x - α) = - 1

Commented by jagoll last updated on 08/Apr/20

thank you sir

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