Book edition 2nd

Author(s) James Stewart

Pages 830 pages

ISBN 9781133112280

Answers without the blur.

Just sign up for free and you're in.

Short Answer

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

The is critical point for the function occurs at \(\frac{4}{3}\).

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given data

The given function is \(g(t) = |3t - 4|\).

Step 2: Concept of Differentiation

Differentiation is a method of finding the derivative of a function. Differentiation is a process, where we find the instantaneous rate of change in function based on one of its variables.

Step 3: Determine the derivative of the function

The given \(g(t)\) is an absolute function. Express the given function as follows.

Obtain the first derivative of the given function \(g(t) = |3t - 4|\).

\(\begin{aligned}{c}g(t) &= \frac{d}{{dt}}\left\{ {\begin{aligned}{*{20}{l}}{3t - 4}&{{\rm{ if }}t \ge \frac{4}{3}}\\{4 - 3t}&{{\rm{ if }}t < \frac{4}{3}}\end{aligned}} \right.\\{g^\prime }(t) &= \left\{ {\begin{aligned}{*{20}{l}}3&{{\rm{ if }}t \ge \frac{4}{3}}\\{ - 3}&{{\rm{ if }}t < \frac{4}{3}}\end{aligned}} \right.\end{aligned}\)

Here, \({g^\prime }(t)\) does not exist at \(t = \frac{4}{3}\) as it cannot be zero ever. Therefore, the only valid critical number occurs at \(t = \frac{4}{3}\) as it satisfies the condition of the definition of critical number. Thus, the only critical number of the function \(g(t) = |3t - 4|\) is \(\frac{4}{3}\).

Find Study Materials for

Create Study Materials

Select your language

Essential Calculus: Early Transcendentals

Answers without the blur.

Short Answer

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

Step by Step Solution

Step 1: Given data

Step 2: Concept of Differentiation

Step 3: Determine the derivative of the function

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Select your language

Essential Calculus: Early Transcendentals

Answers without the blur.

Short Answer

Find the critical numbers of the function.28. \(g(t) = |3t - 4|\)

Step by Step Solution

Step 1: Given data

Step 2: Concept of Differentiation

Step 3: Determine the derivative of the function

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Probability and Statistics

Statistics

Mechanics Maths

Geometry

Pure Maths

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