Let f(x) = x³ + 9x² - 21x + 20. (a) Use the definition of a derivative or the derivative rules to find f'(x) = (b) Use the definition of a derivative or the derivative rules to find ƒ''(x) = For the next parts of the problem, used closed interval notation to enter your answers: (c) ¿On what interval is f increasing (or more specifically, non-decreasing)? interval of increasing = (d) ¿On what interval is f decreasing (or more specifically, non-increasing)? interval of decreasing = (e) ¿On what interval is f concave downward (include the endpoints in the interval)? interval of downward concavity = (f) ¿On what interval is f concave upward (include the endpoints in the interval)? interval of upward concavity =
Let f(x) = x³ + 9x² - 21x + 20. (a) Use the definition of a derivative or the derivative rules to find f'(x) = (b) Use the definition of a derivative or the derivative rules to find ƒ''(x) = For the next parts of the problem, used closed interval notation to enter your answers: (c) ¿On what interval is f increasing (or more specifically, non-decreasing)? interval of increasing = (d) ¿On what interval is f decreasing (or more specifically, non-increasing)? interval of decreasing = (e) ¿On what interval is f concave downward (include the endpoints in the interval)? interval of downward concavity = (f) ¿On what interval is f concave upward (include the endpoints in the interval)? interval of upward concavity =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Kindly use proper Bracket notations.
Use close interval notations where it's neccesary.
Thanks
Transcribed Image Text:Question 6
Let f(x) x³ + 9x² - 21x + 20.
-
<
(a) Use the definition of a derivative or the derivative rules to find
ƒ'(x) =
=
(b) Use the definition of a derivative or the derivative rules to find
f''(x)
>
For the next parts of the problem, used closed interval notation to enter your answers:
(c) ¿On what interval is f increasing (or more specifically, non-decreasing)?
interval of increasing =
(d) ¿On what interval is f decreasing (or more specifically, non-increasing)?
interval of decreasing =
(e) ¿On what interval is f concave downward (include the endpoints in the interval)?
interval of downward concavity
=
=
(f) ¿On what interval is f concave upward (include the endpoints in the interval)?
interval of upward concavity:
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