Let f(x)=- 9x + 18 where f'(x)= Find any x- and y-intercepts of f(x) 18 x²(x+3) (9x+18)² " f"(x)= 162x(x² + 6x +12) (9x+18)³ " Find any horizontal asymptotes of f(x). You should check both y = Lim f(x) & y Lim f(x) though usually same result. Test any HA to see if crossed. X4-8 please do as follows. O Find any vertical asymptotes of f(x). Test any VA to confirm a VA not just a hole. If VA, check behaviour to left and right of VA by finding Lim f(x) & Lim f(x). x→at Final Answer Final Answer VA: Yes No Lim f(x)= Lim f(x) x→a+ = Final Answer
Let f(x)=- 9x + 18 where f'(x)= Find any x- and y-intercepts of f(x) 18 x²(x+3) (9x+18)² " f"(x)= 162x(x² + 6x +12) (9x+18)³ " Find any horizontal asymptotes of f(x). You should check both y = Lim f(x) & y Lim f(x) though usually same result. Test any HA to see if crossed. X4-8 please do as follows. O Find any vertical asymptotes of f(x). Test any VA to confirm a VA not just a hole. If VA, check behaviour to left and right of VA by finding Lim f(x) & Lim f(x). x→at Final Answer Final Answer VA: Yes No Lim f(x)= Lim f(x) x→a+ = Final Answer
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:Curve Sketching (using f(x), f'(x) & f"(x))
Q.#3-Q.#6:
For the f(x), f'(x) & f"(x) provided, please sketch the graph of each f(x) using steps below.
x³
9x + 18
Q.#3 Let f(x) = -
18 x²(x + 3)
(9x+18)²
where f'(x)=-
a) Find any x- and y-intercepts of f(x)
2
f"(x)=
162x(x² +6x+12)
(9x+18)³
please do as follows.
b) Find any vertical asymptotes of f(x). Test any VA to confirm a VA not just a hole.
If VA, check behaviour to left and right of VA by finding Lim f(x) & Lim f(x).
x→a
x→a+
c) Find any horizontal asymptotes of f(x). You should check both y = Lim f(x)
& y= Lim f(x) though usually same result. Test any HA to see if crossed.
X-8
Final Answer
Final Answer
VA: Yes No
Lim f(x)=
x→a
Lim f(x)
x→a+
=
Final Answer
Transcribed Image Text:d) Find any critical points of f(x), determine the intervals on which f(x)
is increasing or decreasing, and classify any relative extrema (relative
maximums & minimums).
e) Find any flex points (points of inflection) of f(x), and determine
the intervals on which f(x) is concave upward or downward.
f) Sketch the graph of f(x), using and labeling the information from (a)-(e).
CPS:
Intervals
Inc.:
Dec.:
Final Answers
Rel. Max:
Rel. Min.:
Final Answers
Possible FPs:
Intervals
Upward:
Downward:
Actual FPS:
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