Question

summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of ( f(x)=\frac{x + 2}{x - 2} ).
find the location of any inflection points of ( f(x) ). select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. there is an inflection point at ( x = ).
(type an integer or a decimal. use a comma to separate answers as needed.)
b. there are no inflection points.
which graph below shows ( f(x) )?

Explanation:

Step1: Find the first derivative

Use the quotient rule \((\frac{u}{v})^\prime=\frac{u^\prime v - uv^\prime}{v^{2}}\). Here \(u = x + 2\), \(u^\prime=1\), \(v=x - 2\), \(v^\prime = 1\).

$$
LATEXBLOCK0
$$

Step2: Find the second derivative

Use the quotient rule again. Let \(u=-4\), \(u^\prime = 0\), \(v=(x - 2)^{2}\), \(v^\prime=2(x - 2)\)

$$
LATEXBLOCK1
$$

Step3: Find inflection points

Set \(f^{\prime\prime}(x)=0\), \(\frac{8}{(x - 2)^{3}}=0\). There is no solution for \(x\) since the numerator \(8
eq0\).

Answer:

B. There are no inflection points.