Applications of Derivatives ML Aggarwal ISC Class-12 Maths Solutions

Applications of Derivatives ML Aggarwal ISC Class-12 Maths Solutions Chapter-7. Step by step Solutions of ML Aggarwal ISC Mathematics Class-12 Exercise 7.1, Exe 7.2 And Exe 7.3, Exe 7.4, Exe 7.5, Exe 7.6, Exe 7.7, Exe 7.8, Exe 7.9, With Chapter Test Questions. Visit official Website CISCE for detail information about ISC Board Class-12 Mathematics.

Applications of Derivatives ML Aggarwal ISC Class-12 Maths Solutions

Board	ISC
Class	12
Subject	Mathematics
Chapter-7	Applications of Derivatives
Session	2024-25
Topics	Solutions of ML Aggarwal

Applications of Derivatives

Rates of Change : The point of this section is to remind us of the application/interpretation of derivatives that we were dealing with in the previous chapter. Namely, rates of change.

Critical Points : In this section we will define critical points. Critical points will show up in many of the sections in this chapter so it will be important to understand them.

Minimum and Maximum Values :

In this section we will take a look at some of the basic definitions and facts involving minimum and maximum values of functions.

Finding Absolute Extrema:

Here is the first application of derivatives that we’ll look at in this chapter. We will be determining the largest and smallest value of a function on an interval.

The Shape of a Graph, Part I:

We will start looking at the information that the first derivatives can tell us about the graph of a function. We will be looking at increasing or decreasing functions as well as the First Derivative Test.

The Shape of a Graph, Part II :

In this section we will look at the information about the graph of a function that the second derivatives can tell us. We will look at inflection points, concavity, and the Second Derivative Test.

Linear Approximations:

Here we will use derivatives to compute a linear approximation to a function. As we will see however, we’ve actually already done this.

Differentials:

We will look at differentials in this section as well as an application for them.

DERIVATIVE AS A RATE MEASURER:-

Derivatives can be used to calculate instantaneous rates of change. The rate of change of position with respect to time is velocity and the rate of change of velocity with respect to time is acceleration. Using these ideas, we’ll be able to analyze one-dimensional particle movement given position as a function of time.

TANGENTS AND NORMALS.

A derivative at a point in a curve can be viewed as the slope of the line tangent to that curve at that point. Given this, the natural next question is what the equation of that tangent line is. Can calculus be used to figure out when a function takes on a local or global maximum value? Absolutely. Not only that, but derivatives and second derivatives can also help us understand the shape of the function (whether they are concave upward or downward). If you have a basic conceptual understanding of derivatives, then you can start applying that knowledge here to identify critical points, extreme, inflections points and even to graph functions