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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.

Respuesta :

SOLUTION:

Given the function;

[tex]f(x)=\frac{x-1}{x-4}[/tex]

(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:

[tex]\begin{gathered} Concave\text{ }Downward:-\infty(d) Inflection point is a point on the graph at which the second derivative is equal to zero or undefined and changes sign.

There are no inflection points.

(e) Asymptotes:

[tex]\begin{gathered} Vertical:x=4 \\ \\ Horizontal:y=1 \end{gathered}[/tex]

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