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Consider the function f(x) = 2x³ – 15x² + 36x +1 over the interval [1,4]. Which statement in below is false? O x = 2 is a local maximum of f over [1,4]. 0x = x = 3 is the absolute minimum of f over [1, 4]. Of attains one absolute maximum over [1,4]. f(3) > 0 O fil(2) × fil(3) ≤ 0

Consider the function f(x) = 2x³ – 15x² + 36x +1 over the interval [1,4]. Which statement in below is false? O x = 2 is a local maximum of f over [1,4]. 0x = x = 3 is the absolute minimum of f over [1, 4]. Of attains one absolute maximum over [1,4]. f(3) > 0 O fil(2) × fil(3) ≤ 0

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter9: Multivariable Calculus
Section9.3: Maxima And Minima
Problem 19E
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**Question:** Consider the function \( f(x) = 2x^3 - 15x^2 + 36x + 1 \) over the interval \([1, 4]\). Which statement below is false? 1. \( x = 2 \) is a local maximum of \( f \) over \([1, 4]\). 2. \( x = 3 \) is the absolute minimum of \( f \) over \([1, 4]\). 3. \( f \) attains one absolute maximum over \([1, 4]\). 4. \( f''(3) > 0 \) 5. \( f''(2) \times f''(3) \lesssim 0 \) **Explanation:** In the image, a mathematical problem is presented wherein a specific cubic function \( f(x) \) is analyzed over a given interval \([1, 4]\). Several statements are listed, and the task is to identify the false statement among them. There are no graphs or diagrams in the image, only a list of textual and mathematical statements. Each statement provides a condition or property related to the function \( f(x) \) at specific points or overall in the given interval. This problem typically involves concepts from calculus, such as finding local and absolute extrema, and analyzing the second derivative to determine concavity and the nature of critical points.
Transcribed Image Text:**Question:** Consider the function \( f(x) = 2x^3 - 15x^2 + 36x + 1 \) over the interval \([1, 4]\). Which statement below is false? 1. \( x = 2 \) is a local maximum of \( f \) over \([1, 4]\). 2. \( x = 3 \) is the absolute minimum of \( f \) over \([1, 4]\). 3. \( f \) attains one absolute maximum over \([1, 4]\). 4. \( f''(3) > 0 \) 5. \( f''(2) \times f''(3) \lesssim 0 \) **Explanation:** In the image, a mathematical problem is presented wherein a specific cubic function \( f(x) \) is analyzed over a given interval \([1, 4]\). Several statements are listed, and the task is to identify the false statement among them. There are no graphs or diagrams in the image, only a list of textual and mathematical statements. Each statement provides a condition or property related to the function \( f(x) \) at specific points or overall in the given interval. This problem typically involves concepts from calculus, such as finding local and absolute extrema, and analyzing the second derivative to determine concavity and the nature of critical points.
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