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The function g is continuous on the closed interval [1, 4] with g(1) = 5 and g(4) = 8. Of the following conditions, which would guarantee that there is a number c in the open interval (1, 4) where g'(c) = 1 ? (A) g is increasing on the closed interval [1, 4]. (B) g is differentiable on the open interval (1, 4). (C) g has a maximum value on the closed interval [1, 4]. (D) The graph of g has at least one horizontal tangent in the open interval (1, 4).

The function g is continuous on the closed interval [1, 4] with g(1) = 5 and g(4) = 8. Of the following conditions, which would guarantee that there is a number c in the open interval (1, 4) where g'(c) = 1 ? (A) g is increasing on the closed interval [1, 4]. (B) g is differentiable on the open interval (1, 4). (C) g has a maximum value on the closed interval [1, 4]. (D) The graph of g has at least one horizontal tangent in the open interval (1, 4).

College Algebra (MindTap Course List)
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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= The function g is continuous on the closed interval [1, 4] with g(1) = 5 and g(4) 8. Of the following conditions, which would guarantee that there is a number c in the open interval (1, 4) where g'(c) = 1 ? (A) g is increasing on the closed interval [1, 4]. (B) g is differentiable on the open interval (1,4). (C) g has a maximum value on the closed interval [1, 4]. (D) The graph of g has at least one horizontal tangent in the open interval (1, 4).
Transcribed Image Text:= The function g is continuous on the closed interval [1, 4] with g(1) = 5 and g(4) 8. Of the following conditions, which would guarantee that there is a number c in the open interval (1, 4) where g'(c) = 1 ? (A) g is increasing on the closed interval [1, 4]. (B) g is differentiable on the open interval (1,4). (C) g has a maximum value on the closed interval [1, 4]. (D) The graph of g has at least one horizontal tangent in the open interval (1, 4).
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