x? – 7x + 12 Consider the function f(æ) x – 5 a. Find the first derivative. f'(x) : b. List any critical values. c. Identify intervals of increase.
x? – 7x + 12 Consider the function f(æ) x – 5 a. Find the first derivative. f'(x) : b. List any critical values. c. Identify intervals of increase.
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter2: Graphical And Tabular Analysis
Section2.1: Tables And Trends
Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...
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Concept explainers
Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
Slope
The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
Question
Transcribed Image Text:x? – 7x + 12
Consider the function f(x) :
x – 5
a. Find the first derivative. f'(x) =
b. List any critical values.
c. Identify intervals of increase.
d. Identify intervals of decrease.
e. Find the second derivaitve. f''(x) =
f. Based on parts b through e, f(x) has a maximum of y
when x =
g. Based on parts b through e, f(x) has a minimum of y
when x =
h. Use the second derivative to identify intervals where f(x) is concave up.
i. Use the second derivative to identify intervals where f(æ) is concave down.
j. Use the second derivative to find any inflection points.
k. State any vertical asymptotes.
I. State any slant asymptotes.
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