Concept explainers
For Exercises 1-12 determine whether each of the following statements is true or false, and explain why.
1. A critical number c is a number in the domain of a function f for which f′(c) = 0 or f'′(c) does not exist.
Whether the given statement is true or false.
Answer to Problem 1RE
The given statement is true.
Explanation of Solution
Given:
A critical number c is a number in the domain of a function f for which
Calculation:
A function can have different shapes on a 2D plane.
The function rises or falls at some numbers from its domain.
At these numbers, the derivative of the function either become zero or does not exists.
The slope around these points is either negative or positive.
Hence, these numbers are called critical numbers as they help to decide whether the function increases or decreases.
Therefore, the statement is true.
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Chapter 13 Solutions
Finite Mathematics And Calculus With Applications:
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