Let gix) be twice differentiable function. Which of the following statements about the function is TRUE? f(x) = g(z)-z² If g'(z) > 4 on [0, 1]. then f(0) is the absolute minimum on [0, 1]. Olf g'(z) <0 on [-1,1], then f(z) is increasing on [-1,1]. Olf 0≤g(z) ≤9 on [2, 4], then f(z) is increasing on [2, 4]. Olf g'(z) <2 on [2,6], then f(6) is the absolute maximum on [2, 6- ○ If g (0) = 0 and g" (0) <0, then z=0 is a local minimum of f(x).
Let gix) be twice differentiable function. Which of the following statements about the function is TRUE? f(x) = g(z)-z² If g'(z) > 4 on [0, 1]. then f(0) is the absolute minimum on [0, 1]. Olf g'(z) <0 on [-1,1], then f(z) is increasing on [-1,1]. Olf 0≤g(z) ≤9 on [2, 4], then f(z) is increasing on [2, 4]. Olf g'(z) <2 on [2,6], then f(6) is the absolute maximum on [2, 6- ○ If g (0) = 0 and g" (0) <0, then z=0 is a local minimum of f(x).
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.
Chapter5: Graphs And The Derivative
Section5.3: Higher Derivatives, Concavity, And The Second Derivative Test
Problem 61E
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![Let g(x) be twice differentiable function. Which of the following statements about
the function
is TRUE?
f(x) = g(z)-z²
Olf g(z) > 4 on [0, 1]. then f(0) is the absolute minimum an [0, 1].
Olf g'(z) <0 on [-1,1], then f(z) is increasing on [-1,1].
Olf 0<g(z) ≤9 on [2, 4], then f(z) is increasing on [2, 4].
Olf g/(z) <2 on [2,6], then f(6) is the absolute maximum on [2,6-
Olf g (0) = 0 and g" (0) <0, then z=0 is a local minimum of f(x).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdbec9372-9d6e-4067-9cf3-23b470681fd7%2F8eec8291-b08f-4802-9901-12634ebdfcd0%2Fezo3bx_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(z)-z²
Olf g(z) > 4 on [0, 1]. then f(0) is the absolute minimum an [0, 1].
Olf g'(z) <0 on [-1,1], then f(z) is increasing on [-1,1].
Olf 0<g(z) ≤9 on [2, 4], then f(z) is increasing on [2, 4].
Olf g/(z) <2 on [2,6], then f(6) is the absolute maximum on [2,6-
Olf g (0) = 0 and g" (0) <0, then z=0 is a local minimum of f(x).
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