So, finding quick and quality solutions online would provide you with tremendous support in progressing with your studies. In Ch 6 Maths Class 12, the introduction part will be a recap of the last chapter where you got acquainted with concepts of derivative of a composite function, implicit functions, logarithmic functions, inverse trigonometric functions and exponential functions.
In this chapter, you will learn how the application of derivatives works in different disciplines like social science, engineering, science, etc. This chapter will go through how to apply the application of derivatives to find out the rate of change of quantities.
Equations of a tangent and normal to a curve at a point. Find out turning points on the graph which will help you determine the points where maximum and minimum values of a function occur.
Find intervals where a function increases and decreases. Approximations and errors. The chapter will also give you ample practice with a variety of exercises of different kinds like short and long answers, objective types questions, etc. You would further expand this concept to find out if changes in x and y are dependent on a 3 rd variable say z i.
In this section of AOD Class 12 NCERT solutions, you would understand what is meant by increasing and decreasing function and how to determine whether a function is increasing or decreasing in a given range by using differentiation.
You would define that a function is increasing in a range if the first derivative is positive in that range. Similarly, you would learn that a function is decreasing in a range if the derivative is negative in that range.
You will learn that in the case of trigonometric functions, one has to determine the quadrant in which they lie in order to know if they are increasing or decreasing. So, in this case, you would understand that for increasing value of x, y is increasing then it is an increasing function, and if y decreases with an increase in the value of x, then it is a decreasing function.
For example, sin x increases in the first quadrant while cos x is a decreasing function in the same quadrant. You would learn that a tangent to a point a,b on a curve is given by:.
With Application of Derivatives Class 12 Solutions, you would get a good idea about what methods to adopt to calculate the expressions utilizing the slope formula. You would get to know how approximations are useful when an exact numerical number is not easy to obtain. You would understand how to derive the approximate value of a quantity that changes in small measures by a change in another variable. From the learnings in this chapter, you will be able to figure out that the derivative of the dependent variable y is not equal to the increase in the variable while the derivative of the independent variable x is equal to the increase in the variable.
You will learn about turning points on the graph of a function where the graph reaches its highest point and the lowest point locally in a domain. You would understand how these points can be used to sketch the graph of a function. You will also be able to find the absolute maximum and absolute minimum of a function which are useful in solving many applied problems. We would learn various definition around maxima and minima which are used for solving problems related to it like:.
The value f p defines the maximum value of f in r, and the point p is termed as the point of the maximum value Byjus Concise Maths Class 9 Answers in r. The value f p defines the maximum value of f in r, and the point p is termed as the point of the minimum value in r.
In a range r, function f is said to have extreme value if there exists a point p in r where f p is either a maximum value or a minimum value of f in r and the point p is termed as the extreme point in r.
You would also learn how local maxima and local minima are represented and many theorems like the first derivative test, second derivative test around this concept. If you want to ace your exams and score well, having solutions to Maths problems becomes essential. Maths is an important subject for boards and also for many competitive exams. Hence if you get the solutions readily available by a stellar team of experts at Vedantu, you have the edge over others.
The solutions are well-crafted by subject matter experts who have given a proper explanation for every step of the problems. Using these solutions, you can get better clarity of the topic and be able to solve even difficult problems with proper time management.
Many tips and tricks of remembering important formulas will be shared. You can always seek assistance from the teachers online in case you get doubts while going through the solutions.
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