📊 CBSE Class 12 2025-26 Sample Paper | Maximize Profit from LED Bulbs | Applications of Derivatives скачать в хорошем качестве

📊 CBSE Class 12 2025-26 Sample Paper | Maximize Profit from LED Bulbs | Applications of Derivatives

In this video we discuss an Applications of Derivatives case study, based on maximization of a function's value, from CBSE Class 12 Sample Paper 2025-26. The question is as follows: LED bulbs are energy-efficient because they use significantly less electricity than traditional bulbs while producing the same amount of light. They convert more energy into light rather than heat, reducing waste. Additionally, their long lifespan means fewer replacements, saving resources and money over time. A company manufactures a new type of energy-efficient LED bulb. The cost of production and the revenue generated by selling x bulbs (in an hour) are modelled as 𝐶(𝑥) = 0.5𝑥^2 − 10𝑥 + 150 and 𝑅(𝑥) = −0.3𝑥^2 + 20𝑥 respectively, where 𝐶(𝑥) and 𝑅(𝑥) are both in ₹. To maximize the profit, the company needs to analyze these functions using calculus. Use the given models to answer the following questions: I. Derive the profit function 𝑃(𝑥) [1] II. Find the critical points of 𝑃(𝑥). [1] III A. Determine whether the critical points correspond to a maximum or a minimum profit by using the second derivative test. OR III B. Identify the possible practical value of 𝑥 (i.e., the number of bulbs that can realistically be produced and sold) that can maximize the profit, if the resources available and the expenditure on machines allows to produce minimum 10 but not more than 18 bulbs per hour. Also calculate the maximum profit. We solve by forming the Profit function P(x) = R(x) - C(x) and then differentiating P(x) and finding the critical points. We also have to check whether the particular critical point(s) give maximum or minimum by taking second derivative test. We find the practically possible x value which gives the maximum profit. Maximum profit is found by substituting this x value in the original profit function. This is an important question for board exam preparation. Keywords: Class 12 Maths Chapter Applications of Derivatives, CBSE Class 12 Maths Sample Question Paper Solution, LED Bulb Profit Problem CBSE, CBSE Class 12 Maths Sample Paper 2025, Class 12 Maths Important Questions, CBSE Class 12 Profit and Cost Problem, Maximum Profit Class 12 Application of Derivatives, Class 12 Board Exam, CBSE Class 12 Maths Previous Year Question Paper Preparation 2025. About us: SD Institute offers online tuitions to students from Class 9 to 12 of both CBSE. Subjects handled: Science and Maths for Classes 9 and 10; Maths, Physics and Chemistry for Classes 12. Website: sdinstitute.co.in You can also contact us for enquiries: 9677025198