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Assume that a function is continuous and is also differentiable on (-infinity, positive infinity). Consider the interval [a,b]; where the a < b are real numbers. state which statement is true or false. If true justify your reasoning on why; if false show an example that indicates why.  a)there is a number c in the interval (a,b) such that f'(c)=0 b) There is a number c for the interval [a,b]; such that f(c) will be the absolute minimum of function on [a,b].

Assume that a function is continuous and is also differentiable on (-infinity, positive infinity). Consider the interval [a,b]; where the a < b are real numbers. state which statement is true or false. If true justify your reasoning on why; if false show an example that indicates why.  a)there is a number c in the interval (a,b) such that f'(c)=0 b) There is a number c for the interval [a,b]; such that f(c) will be the absolute minimum of function on [a,b].

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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Assume that a function is continuous and is also differentiable on (-infinity, positive infinity). Consider the interval [a,b]; where the a < b are real numbers.

state which statement is true or false. If true justify your reasoning on why; if false show an example that indicates why. 

a)there is a number c in the interval (a,b) such that f'(c)=0

b) There is a number c for the interval [a,b]; such that f(c) will be the absolute minimum of function on [a,b]. 

 

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