# Increasing And Decreasing Functions Pdf

By Teodosia J.

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11.05.2021 at 13:11

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Published: 11.05.2021

*In this section we begin to study how functions behave between special points; we begin studying in more detail the shape of their graphs. We start with an intuitive concept. We formally define these terms here.*

If this inequality is strict, i. Similarly, we define a decreasing or non-increasing and a strictly decreasing function. These concepts can be formulated in a more compact form. It is clear that a non-decreasing function can contain strictly increasing intervals and intervals where the function is constant.

## Monotonic function

In this Chapter 17 - Increasing and Decreasing Functions, several exercise questions with solutions for RD Sharma Class 12 Maths are given to help the students and understand the concepts better. We have provided step by step solutions for all exercise questions given in the pdf of Class 12 RD Sharma Chapter 17 - Increasing and Decreasing Functions. All the Exercise questions with solutions in Chapter 17 - Increasing and Decreasing Functions are given below:. Exercise Vedantu academic counsellor will be calling you shortly for your Online Counselling session.

## Increasing and decreasing intervals

In mathematics , a monotonic function or monotone function is a function between ordered sets that preserves or reverses the given order. A function with this property is called strictly increasing. If it is not clear that "increasing" and "decreasing" are taken to include the possibility of repeating the same value at successive arguments, one may use the terms weakly monotone , weakly increasing and weakly decreasing to stress this possibility. The terms "non-decreasing" and "non-increasing" should not be confused with the much weaker negative qualifications "not decreasing" and "not increasing". For example, the function of figure 3 first falls, then rises, then falls again. It is therefore not decreasing and not increasing, but it is neither non-decreasing nor non-increasing. A function that is monotonic, but not strictly monotonic, and thus constant on an interval, doesn't have an inverse.

Derivatives can be used to determine whether a function is increasing, decreasing or constant on an interval: f(x) is increasing if derivative f/(x) > 0, f(x) isβ.

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