Use a computer algebra system to analyze the function over the given interval. f(x) = sin(x) = sin(3x) + sin(5x), [0, π] 1 5 3 (a) Find the first and second derivatives the function. f'(x) = f"(x) = (b) Find any relative extrema and points of inflection. (Round your answers to four decimal places. If an answer does not exist, enter DNE.) relative maximum relative minimum points of inflection smallest x-value smaller x-value larger x-value largest x-value (x, y) = (x, y) = (x, y) = (x, y) = (x, y) = (x, y) = (c) Graph f, f', and f" on the same set of coordinate axes. State the relationship between the behavior of f and the signs of f' and f". The graph of f is increasing when f'-?- 0 and decreasing when f' --?- 0. f is concave upward when f" --?- 0 and concave downward when f" --?-- 0.
Use a computer algebra system to analyze the function over the given interval. f(x) = sin(x) = sin(3x) + sin(5x), [0, π] 1 5 3 (a) Find the first and second derivatives the function. f'(x) = f"(x) = (b) Find any relative extrema and points of inflection. (Round your answers to four decimal places. If an answer does not exist, enter DNE.) relative maximum relative minimum points of inflection smallest x-value smaller x-value larger x-value largest x-value (x, y) = (x, y) = (x, y) = (x, y) = (x, y) = (x, y) = (c) Graph f, f', and f" on the same set of coordinate axes. State the relationship between the behavior of f and the signs of f' and f". The graph of f is increasing when f'-?- 0 and decreasing when f' --?- 0. f is concave upward when f" --?- 0 and concave downward when f" --?-- 0.
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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Question
![Use a computer algebra system to analyze the function over the given interval.
f(x) = sin(x) - sin(3x) + sin(5x), [0, π]
1
3
1
5
(a) Find the first and second derivatives of the function.
f'(x) =
f"(x) =
(b) Find any relative extrema and points of inflection. (Round your answers to four decimal places. If an answer does not exist,
enter DNE.)
relative maximum
relative min num
points of inflection
smallest x-value
smaller x-value
larger x-value
largest x-value
(x, y) =
(x, y) =
(x, y) =
(x, y) =
(x, y) =
(x, y) =
(c) Graph f, f', and f" on the same set of coordinate axes. State the relationship between the behavior of f and the signs of f'
and f".
The graph of f is increasing when f' --?-- 0 and decreasing when f' --?-- 0. f is concave upward when f" --?-- 0
and concave downward when f" --?-- 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F29269e77-b386-4b00-bf00-2788f19e3d90%2Fcccf118a-7c26-4c65-9c5e-6a606d38bbbe%2Fbb7zl8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Use a computer algebra system to analyze the function over the given interval.
f(x) = sin(x) - sin(3x) + sin(5x), [0, π]
1
3
1
5
(a) Find the first and second derivatives of the function.
f'(x) =
f"(x) =
(b) Find any relative extrema and points of inflection. (Round your answers to four decimal places. If an answer does not exist,
enter DNE.)
relative maximum
relative min num
points of inflection
smallest x-value
smaller x-value
larger x-value
largest x-value
(x, y) =
(x, y) =
(x, y) =
(x, y) =
(x, y) =
(x, y) =
(c) Graph f, f', and f" on the same set of coordinate axes. State the relationship between the behavior of f and the signs of f'
and f".
The graph of f is increasing when f' --?-- 0 and decreasing when f' --?-- 0. f is concave upward when f" --?-- 0
and concave downward when f" --?-- 0.
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