Explain why the function has at least one zero in the given interval. C f(x) = x² - 4 - cos(x) [0, π] At least one zero exists because f(x) is continuous and f(0) > 0 while f(z) > 0. At least one zero exists because f(x) is continuous and f(0) < 0 while f(x) < 0. O At least one zero exists because f(x) is continuous and f(0) < 0 while f(z) > 0. At least one zero exists because f(x) being a second degree polynomial must have two real solutions. At least one zero exists because f(x) is not continuous. O Function O Interval
Explain why the function has at least one zero in the given interval. C f(x) = x² - 4 - cos(x) [0, π] At least one zero exists because f(x) is continuous and f(0) > 0 while f(z) > 0. At least one zero exists because f(x) is continuous and f(0) < 0 while f(x) < 0. O At least one zero exists because f(x) is continuous and f(0) < 0 while f(z) > 0. At least one zero exists because f(x) being a second degree polynomial must have two real solutions. At least one zero exists because f(x) is not continuous. O Function O Interval
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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![Explain why the function has at least two zeros in the interval [6, 10].
f(x) = (x8)² - 2
At least two zeros exist because f(x) being a second degree polynomial must have two real solutions.
There are at least two zeros as f(x) is continuous while f(6) < 0, f(8) > 0, and f(10) < 0.
There are at least two zeros as f(x) is continuous while f(6) > 0, f(8) < 0, and f(10) > 0.
O There are at least two zeros as f(x) is continuous while f(6) < 0, f(8) < 0, and f(10) < 0.
At least two zeros exist because f(x) is not continuous on [6, 10].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F147e20c7-f965-40eb-afa0-8f3e744364f8%2Fb50189b5-c936-4c86-bf5b-bf04a6cf0b5f%2F5pdngve_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Explain why the function has at least two zeros in the interval [6, 10].
f(x) = (x8)² - 2
At least two zeros exist because f(x) being a second degree polynomial must have two real solutions.
There are at least two zeros as f(x) is continuous while f(6) < 0, f(8) > 0, and f(10) < 0.
There are at least two zeros as f(x) is continuous while f(6) > 0, f(8) < 0, and f(10) > 0.
O There are at least two zeros as f(x) is continuous while f(6) < 0, f(8) < 0, and f(10) < 0.
At least two zeros exist because f(x) is not continuous on [6, 10].
![Explain why the function has at least one zero in the given interval.
Interval
Function
f(x) = x² - 4 - cos(x) [0, π]
At least one zero exists because f(x) is continuous and f(0) > 0 while f(z) > 0.
At least one zero exists because f(x) is continuous and f(0) < 0 while f(n) < 0.
O At least one zero exists because f(x) is continuous and f(0) < 0 while f(z) > 0.
At least one zero exists because f(x) being a second degree polynomial must have two real solutions.
At least one zero exists because f(x) is not continuous.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F147e20c7-f965-40eb-afa0-8f3e744364f8%2Fb50189b5-c936-4c86-bf5b-bf04a6cf0b5f%2Fd1nunp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Explain why the function has at least one zero in the given interval.
Interval
Function
f(x) = x² - 4 - cos(x) [0, π]
At least one zero exists because f(x) is continuous and f(0) > 0 while f(z) > 0.
At least one zero exists because f(x) is continuous and f(0) < 0 while f(n) < 0.
O At least one zero exists because f(x) is continuous and f(0) < 0 while f(z) > 0.
At least one zero exists because f(x) being a second degree polynomial must have two real solutions.
At least one zero exists because f(x) is not continuous.
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