CBSE 12th Application of Derivatives Repeated Questions 2025: 10 Important PYQ

CBSE 12th Application of Derivatives Repeated Questions 2025: The Central Board of Secondary Education (CBSE) will conduct the Class 12 Mathematics 2025 examination on March 8, 2025. Mathematics being one of the toughest subjects needs resilience and practice to score good marks. Students must strategically prepare for the examination. To do so, it is important to solve the previous year's question papers. As the Calculus chapter holds the highest weightage of 35 marks, it is crucial to understand what kind of questions will be asked in the examination. Students can check the CBSE 12th Application of Derivatives Repeated Questions 2025 available here.

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CBSE 12th Application of Derivatives Repeated Questions 2025

Students can get the 10 important CBSE Class 12 Application of Derivatives Repeated Questions 2025 below.

1. The total cost C(x) associated with the production of x units of an item is given by C(x) = 0.005x³ – 0.02x² + 30x + 5000. Find the marginal cost when 3 units are produced, where by marginal cost we mean the instantaneous rate of change of total cost at any level of output. (CBSE 2018)
   Answer: 30.015
   
   
2. The total revenue received from the sale of x units of a product is given by R(x) = 3x2 + 36x + 5 in rupees. Find the marginal revenue when x = 5, where by marginal revenue we mean the rate of change of total revenue concerning the number of items sold at an instant. (CBSE 2018 C)
   Answer: Marginai Revenue (MR) = 6 × 5 + 36 = 66
   
   
3. The volume of a sphere is increasing at the rate of 8 cm3/s. Find the rate at which its surface area is increasing when the radius of the sphere is 12 cm. (CBSE 2017 C)
   Answer: 4/3 cm²/s
4. Show that the function f(x) = x3 – 3x2 + 6x – 100 is increasing on R. (CBSE 2017)
   Answer: f'(x) > 0. This shows that function f(x) is increasing on R. Hence proved.
   
   
5. Find the intervals in which the function
   f(x) = x44 – x³ – 5x² + 24x + 12 is
   (i) strictly increasing
   (ii) strictly decreasing. (CBSE 2018)
   Answer: f(x) is strictly increasing in the intervals (-3, 2) and (4, ∞), and strictly decreasing in the intervals (-∞, -3) and (2, 4).
   
   
6. Find the intervals in which the function f(x) = 3x⁴ – 4x³ – 12x² + 5 is
   (i) strictly increasing.
   (ii) strictly decreasing. (CBSE 2014)
    Answer: if f'(x) < 0, then it is strictly decreasing.
   f(x) = 3x⁴ – 4x³ – 12x² + 5
   On differentiating both sides w.r.t. x, we get
   f'(x) = 12x³ -12x² – 24x
   For strictly increasing or strictly decreasing, put f'(x) = 0, we get
   12x³ – 12x² – 24x = 0
   ⇒ 12x [x² – 2x + x – 2] = 0
   12x (x + 1) (x – 2) = 0
   ∴ x = 0, -1 or 2
   
   
7. Find the intervals in which the function is given by ;
   f(x) = 310 x⁴ – 45x³ – 3x² + 36x5 + 11 is
   (i) strictly increasing.
   (ii) strictly decreasing. (CBSE 2014C)
   Answer:
   (i) Strictly increasing in (-2, 1) and (3, ∞).
   (ii) Strictly decreasing in (-∞,- 2) and (1, 3).
   
   
8. The sides of an equilateral triangle are increasing at the rate of 2 cm/s. Find the rate at which the area increases when the side is 10 cm. (CBSE 2010C)
   Answer: 10√ 3 cm²/s 
   
   
9. Find the intervals in which the function
   f(x) = 32 x⁴ – 4x³ – 45x² + 51 is
   (i) strictly increasing.
   (ii) strictly decreasing. (CBSE 2012C)
   Answer:
   (i) Strictly increasing in (-3, 0) and (5, ∞).
   (ii) Strictly decreasing in (-∞,- 3) and (0,5).
   
   
10. Find the intervals in which the function
    f(x) = 2x³ – 9x² + 12x -15 is
    (i) increasing.
    (ii) decreasing. (CBSE 2011)
    Answer:
    (i) The function increases on intervals (- ∞, 1]and [2, ∞).
    (ii) The function decreasing on the interval [1, 2]

Students are advised to go through the above questions and answers to prepare well for the CBSE Class 12 Examination 2025. Visit the official website of the Central Board of Secondary Education (CBSE) for more information.