Determine any local (or relative) extrema of f(x) as ordered pairs. [You may roundany values to three decimal places. If there are more answer spaces than necessary,leave the extra spaces unanswered.]f(x) has a local Select an answer atf(x) has a local | Select an answer atf(x) has a local Select an answer atUse calculus to determine the interval(s) where f(x) is concave up and the intervalswhere f(x) is concave down.f(x) is concave up onf(x) is concave down onDetermine any inflection points of f(x) as ordered pairs. [You may round any valuesto three decimal places.]Inflection Point (s) at:Use your work from the previous parts to create a rough sketch of the graph off(x) = 2 +-3-2/2 = 2x² +30=9 9 on your work paper. Use appropriate scale onxthe axes. Do your best to include the important features you have found through youranalysis. Do not input anything in the answerbox below 3We want to sketch the function f(x) = 2 +xNote that f'(x) =State the domain of f(x).Domain:x-intercept(s):y-intercept(s):limx →3 18+lim=x →-3x+18.Use algebra to determine any intercepts of f(x). Write the intercepts as orderedpairs.9--2f(x) =Behavior on the right of the vertical asymptote:22x + 3x9.xand f''(x)Locate any horizontal asymptote of f(x) by using limits. Write any horizontalasymptote as an equation.Horizontal Asymptote:f(x) is decreasing onState the location of the vertical asymptote of f(x) and use limits to describe thebehavior of the function on each side of the asymptote.Location of Vertical Asymptote:Behavior on the left of the vertical asymptote:f(x)=6546x 54xUse calculus to determine the interval(s) where f(x) is increasing and the intervalswhere f(x) is decreasing.f(x) is increasing on

Since you have asked multiple sub parts in a single request so we will be answering only first three…

3 We want to sketch the function f(x) = 2 + Note that f'(z) = State the domain of f(z). Domain: z-intercept(s): 3 18 + y-intercept(s): -3x + 18 -2-20²+3x-9. and f''(z) = 6 Use algebra to determine any intercepts of f(x). Write the intercepts as ordered pairs. 54 бæ - 54 Locate any horizontal asymptote of f(x) by using limits. Write any horizontal asymptote as an equation. Horizontal Asymptote: State the location of the vertical asymptoto of sin and uro limite to describe the

3 We want to sketch the function f(x) = 2 + Note that f'(z) = State the domain of f(z). Domain: z-intercept(s): 3 18 + y-intercept(s): -3x + 18 -2-20²+3x-9. and f''(z) = 6 Use algebra to determine any intercepts of f(x). Write the intercepts as ordered pairs. 54 бæ - 54 Locate any horizontal asymptote of f(x) by using limits. Write any horizontal asymptote as an equation. Horizontal Asymptote: State the location of the vertical asymptoto of sin and uro limite to describe the

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

Determine any local (or relative) extrema of f(x) as ordered pairs. [You may round
any values to three decimal places. If there are more answer spaces than necessary,
leave the extra spaces unanswered.]
f(x) has a local Select an answer at
f(x) has a local | Select an answer at
f(x) has a local Select an answer at
Use calculus to determine the interval(s) where f(x) is concave up and the intervals
where f(x) is concave down.
f(x) is concave up on
f(x) is concave down on
Determine any inflection points of f(x) as ordered pairs. [You may round any values
to three decimal places.]
Inflection Point (s) at:
Use your work from the previous parts to create a rough sketch of the graph of
f(x) = 2 +
-3-2/2 = 2x² +30=9 9 on your work paper. Use appropriate scale on
x
the axes. Do your best to include the important features you have found through your
analysis. Do not input anything in the answerbox below

3
We want to sketch the function f(x) = 2 +
x
Note that f'(x) =
State the domain of f(x).
Domain:
x-intercept(s):
y-intercept(s):
lim
x →
3 18
+
lim
=
x →
-3x+18.
Use algebra to determine any intercepts of f(x). Write the intercepts as ordered
pairs.
9
--2
f(x) =
Behavior on the right of the vertical asymptote:
2
2x + 3x9.
x
and f''(x)
Locate any horizontal asymptote of f(x) by using limits. Write any horizontal
asymptote as an equation.
Horizontal Asymptote:
f(x) is decreasing on
State the location of the vertical asymptote of f(x) and use limits to describe the
behavior of the function on each side of the asymptote.
Location of Vertical Asymptote:
Behavior on the left of the vertical asymptote:
f(x)
=
6
54
6x 54
x
Use calculus to determine the interval(s) where f(x) is increasing and the intervals
where f(x) is decreasing.
f(x) is increasing on

Expert Solution

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Step 1: Determine the given function

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Step 2: Drawing the graph of the given function

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Step 3: Finding the domain of the given function

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Step 4: Finding the intercepts

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Step 5: Finding the horizontal asymptotes

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Follow-up Questions

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Follow-up Question

State the location of the vertical asymptote of \( f(x) \) and use limits to describe the behavior of the function on each side of the asymptote.

- **Location of Vertical Asymptote:** \_\_\_\_\_

- **Behavior on the left of the vertical asymptote:**
\[
\lim_{{x \to \_\_\_\_^-}} f(x) = \_\_\_\_
\]

- **Behavior on the right of the vertical asymptote:**
\[
\lim_{{x \to \_\_\_\_^+}} f(x) = \_\_\_\_
\]

---

Use calculus to determine the interval(s) where \( f(x) \) is increasing and the intervals where \( f(x) \) is decreasing.

- \( f(x) \) is increasing on \_\_\_\_\_

- \( f(x) \) is decreasing on \_\_\_\_\_

---

Determine any local (or relative) extrema of \( f(x) \) as ordered pairs. [You may round any values to three decimal places. If there are more answer spaces than necessary, leave the extra spaces unanswered.]

- \( f(x) \) has a local \(\text{[Select an answer]}\) at \_\_\_\_\_.

- \( f(x) \) has a local \(\text{[Select an answer]}\) at \_\_\_\_\_.

- \( f(x) \) has a local \(\text{[Select an answer]}\) at \_\_\_\_\_.

---

Use calculus to determine the interval(s) where \( f(x) \) is concave up and the intervals where \( f(x) \) is concave down.

- \( f(x) \) is concave up on \_\_\_\_\_

- \( f(x) \) is concave down on \_\_\_\_\_

---

Determine any inflection points of \( f(x) \) as ordered pairs. [You may round any values to three decimal places.]

- Inflection Point(s) at: \_\_\_\_\_

---

Use your work from the previous parts to create a rough sketch of the graph of
\[
f(x) = 2 + \frac{3}{x} - \frac{9}{x^2} = \frac{2x^

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