RD Sharma Class 12 Solutions Chapter 18 - Maxima and Minima (Ex 18.1) Exercise 18.1 - Free PDF
FAQs on RD Sharma Class 12 Solutions Chapter 18 - Maxima and Minima (Ex 18.1) Exercise 18.1
1. Where can I find reliable, step-by-step solutions for RD Sharma Class 12 Maths Chapter 18, Exercise 18.1?
Vedantu provides comprehensive, step-by-step solutions for all problems in RD Sharma Class 12 Maths Chapter 18 (Maxima and Minima), Exercise 18.1. These solutions are prepared by expert teachers and are fully aligned with the latest CBSE guidelines for the 2025-26 academic year, ensuring you understand the correct methodology for solving each question.
2. What is the fundamental method used to solve the problems in RD Sharma Class 12 Ex 18.1 on Maxima and Minima?
The problems in Exercise 18.1 are primarily solved using the First Derivative Test. This involves finding the critical points of a function (where the derivative is zero or undefined) and then analysing the sign of the first derivative, f'(x), around these points to determine if they correspond to a local maximum, a local minimum, or a point of inflection.
3. How do you determine if a critical point is a local maximum or a local minimum using the method for Ex 18.1?
To determine the nature of a critical point 'c' using the first derivative test, you check the sign of f'(x) on either side of 'c':
- If f'(x) changes its sign from positive to negative as x increases through c, then the function has a local maximum at c.
- If f'(x) changes its sign from negative to positive as x increases through c, then the function has a local minimum at c.
- If f'(x) does not change sign, c is a point of inflection and is neither a maximum nor a minimum.
4. Are the methods in Vedantu's RD Sharma solutions for Ex 18.1 sufficient for the CBSE board exams?
Yes, absolutely. The methods detailed in our solutions for RD Sharma Class 12 Ex 18.1 are fully aligned with the CBSE 2025-26 syllabus and marking scheme. They emphasise the step-by-step approach required to score full marks in board examinations, focusing on the application of the First Derivative Test as prescribed in the NCERT curriculum.
5. Why is it important to find all critical points, not just where the derivative is zero?
While many problems focus on points where the derivative is zero (stationary points), it's crucial to also check for points where the derivative is undefined. These are also critical points and can correspond to a maximum or minimum, often appearing as sharp corners or cusps on a function's graph. Overlooking these points can lead to an incomplete analysis and missing a potential extremum.
6. What is the key difference between a local extremum and an absolute extremum in this chapter?
A local maximum or minimum is the highest or lowest point within a specific, small interval of the function. A function can have several local extrema. In contrast, an absolute maximum or minimum is the single highest or lowest point across the function's entire given domain. The initial exercises like Ex 18.1 focus on finding local extrema, which is a foundational step for later finding absolute extrema in a closed interval.
7. How can a student avoid common mistakes while solving problems from RD Sharma Ex 18.1?
To avoid common errors, students should focus on the following:
- Correctly differentiate the function, as any error here invalidates the subsequent steps.
- Ensure all critical points are found by solving f'(x) = 0 and also checking where f'(x) is not defined.
- Be meticulous when analysing the sign change of the derivative. Use a number line and test points to the immediate left and right of each critical point.
- Remember to state the final answer clearly by providing both the point of maxima/minima (the x-value) and the corresponding maximum/minimum value of the function (the y-value).
