Using the graphing utility, graph the function y = . f'(x). f'(x) = x – 16x³ + 81x² – 146x + 80

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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Using the graphing utility, graph the function y = f'(x).
f'(x) = x – 16x³ + 81x? – 146x + 80
f' (x) =
,4 – 16x³ + 81x?
- 146x + 80
40
y
+
20
-2
4
10
-20
--40
-60
-80
powered by
desmos
-100
Use the graph to find the point(s) of inflection of f.
(Give your answer in the form of a comma-separated list of values. Express numbers in exact form. Use symbolic
notation and fractions where needed. Enter DNE if the function has no inflection points.)
Use the graph to determine the interval(s) on which the function f is concave down.
(Give your answer as an interval in the form (*, *). Use the symbol o for infinity, U for combining intervals, and an
appropriate type of parenthesis "(",")", "[","]" depending on whether the interval is open or closed. Enter Ø if the interval
is empty. Use decimal notation. Give your numbers to three decimal places.)
interval(s):
Transcribed Image Text:Using the graphing utility, graph the function y = f'(x). f'(x) = x – 16x³ + 81x? – 146x + 80 f' (x) = ,4 – 16x³ + 81x? - 146x + 80 40 y + 20 -2 4 10 -20 --40 -60 -80 powered by desmos -100 Use the graph to find the point(s) of inflection of f. (Give your answer in the form of a comma-separated list of values. Express numbers in exact form. Use symbolic notation and fractions where needed. Enter DNE if the function has no inflection points.) Use the graph to determine the interval(s) on which the function f is concave down. (Give your answer as an interval in the form (*, *). Use the symbol o for infinity, U for combining intervals, and an appropriate type of parenthesis "(",")", "[","]" depending on whether the interval is open or closed. Enter Ø if the interval is empty. Use decimal notation. Give your numbers to three decimal places.) interval(s):
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