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Critical Numbers What is a critical number?

   Critical Numbers What is a critical number?

Calculus of a Single Variable

Calculus of a Single Variable

Ron Larson 11th Edition

Chapter 3, Problem 4

Instant Answer

Solved by Expert Arushi Sahay

06/18/2019

Step 1

A function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. In other words, for every value of $x$, there is a corresponding value of $f(x)$. Show more…

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Critical Numbers What is a critical number?

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Key Concepts

Derivative

The derivative of a function represents the rate of change or the slope of the function at any given point. It is used to determine the increasing or decreasing behavior of functions and plays a crucial role in finding critical numbers by indicating where the slope is zero or undefined.

Domain of a Function

The domain of a function consists of all the input values for which the function is defined. In the context of critical numbers, it is important that the candidate point is within the domain, as only then can it be considered for further analysis regarding local extrema or other types of behavior.

Critical Number

A critical number of a function is an input value within the domain where the function's derivative is zero or the derivative does not exist. This concept is fundamental in calculus as it helps identify points at which the function might have local maxima, minima, or other significant behavior changes.

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