Q. 12 - Calculus

Question

Moreover, the following properties follow from this definition (fill in the blanks or select the correct options): 

$\ln x$ is (increasing)/(decreasing) on its entire domain and (concave up)/(concave down) on its entire domain.

Step-by-Step Solution

Answer

The correct statement is, 

$\ln x$ is increasing on its entire domain and concave down on its entire domain.

Step 1. Given information.

We are given an incomplete statement, 

$\ln x$ is (increasing)/(decreasing) on its entire domain and (concave up)/(concave down) on its entire domain. 

Step 2. Completing the statement.

We know that,

$\ln x$ is increasing on its entire domain $(0,\infty )$ and concave down on its entire domain $(0,\infty )$.