Let g(x) be twice differentiable function. Which of the following statements abou the function is TRUE? f(x) = g(x)+x² If g'(x) <3 on (0, 2), then f(0) is the absolute minimum on [0,2]. If g'(x) <-2 on [0, 1], then f(x) is increasing on [0, 1]. If g'(x) > 0 on [1, 10], then f(10) is the absolute maximum on [1, 10]. If g'(x) < 0 on [-5, -1], then f(x) is increasing on-5, -1]. If g'(0) = 0 and g" (0) > 0, then x = 0 is a local maximum of f(x).
Let g(x) be twice differentiable function. Which of the following statements abou the function is TRUE? f(x) = g(x)+x² If g'(x) <3 on (0, 2), then f(0) is the absolute minimum on [0,2]. If g'(x) <-2 on [0, 1], then f(x) is increasing on [0, 1]. If g'(x) > 0 on [1, 10], then f(10) is the absolute maximum on [1, 10]. If g'(x) < 0 on [-5, -1], then f(x) is increasing on-5, -1]. If g'(0) = 0 and g" (0) > 0, then x = 0 is a local maximum of f(x).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Let g(x) be twice differentiable function. Which of the following statements about
the function
is TRUE?
f(x) = g(x)+x²
If g'(x) <3 on (0, 2), then f(0) is the absolute minimum on [0,2].
If g'(x) <-2 on [0, 1], then f(x) is increasing on [0, 1].
If g'(x)>0 on [1, 10], then f(10) is the absolute maximum on [1, 10].
If g'(x) <0 on [-5, -1], then f(x) is increasing on-5, -1].
If g'(0) = 0 and g" (0) > 0, then x = 0 is a local maximum of f(x).
-](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fca8c17e0-57f7-40c8-b68b-bcb6c5953aaf%2Fa7c8c07e-7882-4580-82d6-5317989ea67e%2F6ptv9zm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let g(x) be twice differentiable function. Which of the following statements about
the function
is TRUE?
f(x) = g(x)+x²
If g'(x) <3 on (0, 2), then f(0) is the absolute minimum on [0,2].
If g'(x) <-2 on [0, 1], then f(x) is increasing on [0, 1].
If g'(x)>0 on [1, 10], then f(10) is the absolute maximum on [1, 10].
If g'(x) <0 on [-5, -1], then f(x) is increasing on-5, -1].
If g'(0) = 0 and g" (0) > 0, then x = 0 is a local maximum of f(x).
-
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