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

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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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].
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.
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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