Only answer interval of increase or decrease and equation of asymptote

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asked Aug 14, 2023 147k views

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Jllopezpino · Answer 1 · 2023-08-21T15:28:05+0000

Solution

Given the function

$f(x)=-\log\lbrack-(x-5)\rbrack+4$

Domain

setting -(x - 5)>0

=> x - 5 < 0

=> x < 5

$D=\lbrace x\text{ \mid}x<5\rbrace$

Taking the derivative of f(x) with respect to x

$\begin{gathered} f^(\prime)(x)=-(1)/((x-5)\ln10) \\ \\ \text{ setting }f^(\prime)(x)=0 \\ \\ \text{ The critical point is }x=5\text{ since }f^(\prime)(5)\text{ is undefined.} \end{gathered}$

Hence the interval of Decrease is

$(-\infty,5)$

The equation of asymptote is x =5

Only answer interval of increase or decrease and equation of asymptote

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