NCERT Class 12 · Ch 6 Exercise 6.3 · Q13
NCERT Class 12 Maths · Chapter 6 Applications Of Derivatives · Exercise 6.3 Question 13
Find two numbers with sum 24 and maximum product.
💡 Concept Hints
- Identify the domain and the inner and outer functions, or the relevant one-sided limits.
- Apply the appropriate differentiation or limit rule, keep all chain factors, and check exceptional points.
✅ Step-by-Step Solution
Final Answer: 12 and 12; maximum product 144.
- Use the fixed sum to express the second number in terms of x. The objective is \(x \left(24 - x\right)\) on R.
- Differentiate: \(- 2 \left(x - 12\right)\). The feasible interior stationary point is x=12.
- The second derivative there is \(-2\). Completing the square or the derivative sign change confirms the global extremum.
Master Chapter 6: Applications Of Derivatives
Practise interactive questions, flashcards, visual mind maps, and timed board tests for Applications Of Derivatives.
← Previous Question
Find maximum and minimum of x+sin 2x on [0,2π].
Next Question →Find positive x,y with x+y=60 maximizing xy³.
All Questions in Applications Of Derivatives — Exercise 6.3
Related Questions in Applications Of Derivatives
Class 12 Applications Of Derivatives · Mcq Single Correct
Find the maximal open interval on which f(x)=x²e^(−x) has positive derivative.
Class 12 Applications Of Derivatives · Mcq Single Correct
For f(x)=x²−4x+6, identify the maximal open interval where f′(x)>0.
Class 12 Applications Of Derivatives · Mcq Single Correct
For x>0, at which x is f(x)=x^x stationary?
Class 12 Applications Of Derivatives · Mcq Single Correct
Find the maximum value of (1/x)^x for x>0.
Class 12 Applications Of Derivatives · Mcq Single Correct
Find the maximum of [x(x−1)+1]^(1/3) on 0≤x≤1.
Class 12 Applications Of Derivatives · Mcq Single Correct
A trapezium area model is A(x)=(10+x)√(100−x²) cm² for 0≤x≤10. Find its maximum.