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Let f(x) = x³ + 3x² - 24x + 18. (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 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 =

Let f(x) = x³ + 3x² - 24x + 18. (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 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 =

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section: Chapter Questions
Problem 15T
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Let f(x) = x³ + 3x² - 24x + 18. (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 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 =
Transcribed Image Text:Let f(x) = x³ + 3x² - 24x + 18. (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 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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