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Given f(x) = (x-1)/ (x-4), find the following:a. critical points, b. intervals of increase/decrease, c. intervals of concavity,d. inflection points e. all asymptotes.

User Breanna
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1 Answer

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20 votes

SOLUTION:

Given the function;


f(x)=(x-1)/(x-4)

(a) Critical points are points where the function is defined and its derivative is zero or undefined.

ANSWER: The function has no critical points.

(b) Intervals of increase/decrease:

(c) Intervals of concavity:


\begin{gathered} Concave\text{ }Downward:-\infty<strong>(d) Inflection point </strong>is a point on the graph at which the second derivative is equal to zero or undefined and changes sign.<p></p><p><strong>There are no inflection points.</strong></p><p><strong>(e) Asymptotes:</strong></p>[tex]\begin{gathered} Vertical:x=4 \\ \\ Horizontal:y=1 \end{gathered}

Given f(x) = (x-1)/ (x-4), find the following:a. critical points, b. intervals of-example-1
User GeoB
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