Question

Find the critical numbers of the function. $g(t)=|3 t-4|$

   Find the critical numbers of the function.
$g(t)=|3 t-4|$

Calculus

James Stewart 7th Edition

Chapter 3, Problem 34

Instant Answer

Solved by Expert Souvik Ghosh

06/17/2020

Step 1

Step 1: Recall that the critical numbers of a function are the values in the domain where either the derivative equals zero or the derivative does not exist. Show more…

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Find the critical numbers of the function. $g(t)=|3 t-4|$

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Key Concepts

Absolute Value Function

An absolute value function, expressed in the form f(x) = |x|, always yields non-negative outputs. Its graph typically features a sharp corner at the point where the argument equals zero, which is often a location of non-differentiability.

Piecewise Definition and Differentiability

Absolute value functions can be rewritten as piecewise functions to facilitate differentiation. By defining the function separately on intervals determined by the sign of the expression inside the absolute value, one can compute derivatives on each interval individually. Special care is needed at the boundary points where the function pieces meet, as these are common spots where the derivative may fail to exist.

Critical Numbers

Critical numbers are the values in the domain of a function where its derivative is either zero or does not exist. These points are especially significant in calculus because they can signal the presence of local extrema or changes in the behavior of the function.

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