Explanation Given: Consider the function, f ( x ) = ln x . Definition used: Increasing function: Let f be a function with its derivative defined on some interval. Then the function is said to be increasing if the inequality f ( x ) > 0 holds for every x in the interval. Decreasing function: Let f be a function with its derivative defined on some interval. Then the function is said to be decreasing if the inequality f ( x ) < 0 holds for every x in the interval. Calculation: Use online graphing calculator and obtain the graph of f ( x ) = ln x as shown below in Figure 1. From Figure 1, it is observed that the graph f ( x ) = ln x increases everywhere and the graph f ( x ) = ln x does not decrease in any interval. Obtain the derivative of the function f ( x ) = ln x as follows

Finite Mathematics and Calculus with Applications (10th Edition)

10th Edition

ISBN: 9780321979407

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 13.1, Problem 41E

To determine

To find: The intervals where f(x)=lnx increases and decreases, and also where the tangent line is horizontal.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 13.1, Problem 40E

Chapter 13.1, Problem 42E

Students have asked these similar questions

Find and classify the critical points of z = (x² – 8x) (y² – 6y). Local maximums: Local minimums: Saddle points: - For each classification, enter a list of ordered pairs (x, y) where the max/min/saddle occurs. Enter DNE if there are no points for a classification.

Suppose that f(x, y, z) = (x − 2)² + (y – 2)² + (z − 2)² with 0 < x, y, z and x+y+z≤ 10. 1. The critical point of f(x, y, z) is at (a, b, c). Then a = b = C = 2. Absolute minimum of f(x, y, z) is and the absolute maximum is

The spread of an infectious disease is often modeled using the following autonomous differential equation: dI - - BI(N − I) − MI, dt where I is the number of infected people, N is the total size of the population being modeled, ẞ is a constant determining the rate of transmission, and μ is the rate at which people recover from infection. Close a) (5 points) Suppose ẞ = 0.01, N = 1000, and µ = 2. Find all equilibria. b) (5 points) For the equilbria in part a), determine whether each is stable or unstable. c) (3 points) Suppose ƒ(I) = d. Draw a phase plot of f against I. (You can use Wolfram Alpha or Desmos to plot the function, or draw the dt function by hand.) Identify the equilibria as stable or unstable in the graph. d) (2 points) Explain the biological meaning of these equilibria being stable or unstable.

Chapter 13 Solutions

Finite Mathematics and Calculus with Applications (10th Edition)

Ch. 13.1 - Find where the function is increasing and...Ch. 13.1 - Prob. 2YT Ch. 13.1 - Prob. 3YT Ch. 13.1 - Prob. 4YT Ch. 13.1 - Prob. 1WE Ch. 13.1 - Prob. 2WE Ch. 13.1 - Prob. 3WE Ch. 13.1 - Prob. 4WE Ch. 13.1 - Prob. 5WE Ch. 13.1 - Prob. 6WE

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

The intervals where f ( x ) = ln x increases and decreases, and also where the tangent line is horizontal.

Solution Summary: The author explains how the function f(x)=mathrmlnx increases everywhere, decreases nowhere, and the tangent is nowhere horizontal on the graph.

Videos

To find: The intervals where f(x)=lnx increases and decreases, and also where the tangent line is horizontal.

Want to see the full answer?

Chapter 13 Solutions