Let g(x) be twice differentiable function. Which of the following statements about the function is TRUE? f(x) = g(x) + x² If g'(0) = 0 and g″(0) > 0, then x = 0 is a local maximum of f(x). ○ If g'(x) < 0 on [−5, −1], then ƒ(x) is increasing on [–5, −1]. If g'(x) < −2 on [0, 1], then f(x) is increasing on [0, 1]. ○ If g'(x) < −3 on (0, 2), then ƒ(0) is the absolute minimum on [0, 2]. ○ If g'(x) > 0 on [1, 10], then ƒ(10) is the absolute maximum on [1, 10].

Let g(x) be twice differentiable function. Which of the following statements about the function is TRUE? f(x) = g(x) + x² If g'(0) = 0 and g″(0) > 0, then x = 0 is a local maximum of f(x). ○ If g'(x) < 0 on [−5, −1], then ƒ(x) is increasing on [–5, −1]. If g'(x) < −2 on [0, 1], then f(x) is increasing on [0, 1]. ○ If g'(x) < −3 on (0, 2), then ƒ(0) is the absolute minimum on [0, 2]. ○ If g'(x) > 0 on [1, 10], then ƒ(10) is the absolute maximum on [1, 10].

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter3: Functions

Section3.3: More On Functions; Piecewise-defined Functions

Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...

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