RD Sharma Solutions for Class 12 Maths Chapter 13 - Derivative as a Rate Measurer - Free PDF Downlaod
FAQs on RD Sharma Class 12 Maths Solutions Chapter 13 - Derivative as a Rate Measurer
1. What does the derivative of a rate mean?
The instantaneous rate of change is the measurement of the rate of change, or slope, of a curve at a certain instant. Thus, the instantaneous rate of change is related to the derivative. A derivative is a tool used to calculate the instantaneous rate of change of a variable with respect to another variable. The first-order derivative gives the slope of a tangent line. The average rate of change is different from the instantaneous rate of change. While the former gives the slope of the secant line which is usually calculated by algebraic formula the latter i.e. instantaneous rate of change gives the slope of the tangent line using derivatives.
2. What is the rate of change of y with respect to x, satisfying the rule y = f(x)?
The rate of change of y with respect to x means how much y changes per unit change in x. This means y is a function of x. Hence any change in x causes a change in rate. Here, the rate of change of y can be found by taking the derivative of the original function y. It can be represented graphically also. The slope of the tangent line of the graph of y is plotted at the point where x=[x_{0}].
3. How do derivatives help in business?
Derivative has many real-life applications. Loss or profit in business can be calculated by derivatives. Derivatives are needed to maximize profit in business. Derivative of total profit with respect to the quantity has to be determined. This can be the way to find the profit-maximizing output. The derivative is taken as zero and quantity q is solved. Then the profit-maximizing quantity q is substituted with the demand value in the demand equation to get the value for profit output P. This way derivatization helps to get the maximum profit in business.
4. What are the applications of Derivative as a Rate Measure?
It is used to determine a new value of a quantity from the old value and the amount of change.
It helps us to calculate the average rate of change and explains how it differs from the instantaneous rate of change.
We can apply rates of change to the displacement, velocity, and acceleration of an object moving along a straight line.
It is also used to predict the future population from the present value and the population growth rate.
Derivatives are used to calculate marginal cost and revenue in a business situation.
5. How Vedantu helps the students in the Chapter of Derivative as a Rate Measure?
These solutions are formulated by Vedantu experts in an interactive manner to create interest in learning among students. Solutions provided by RD Sharma also contain explanatory diagrams and tables for comparative study, which makes it easy to learn the crucial topics. Students who find difficulty in solving these topics are suggested to go through solutions provided by RD Sharma. These solutions are prepared from the exam point of view and according to the latest syllabus. Vedantu also provides sample papers based on previous year’s questions on this topic to boost confidence regarding this topic among the students of Class 12.
