NCERT Class 12 · Ch 6 Exercise 6.3 · Q22
NCERT Class 12 Maths · Chapter 6 Applications Of Derivatives · Exercise 6.3 Question 22
Cut 28 m wire into a square perimeter and circle circumference to minimize their combined area.
💡 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: Square piece 112/(π+4) m; circle piece 28π/(π+4) m.
- Let x be the square piece, 0≤x≤28. The square area is x²/16 and the circle area is (28−x)²/(4π).
- A′=x/8−(28−x)/(2π). Set it to zero: πx=4(28−x), hence x=112/(π+4).
- A″=1/8+1/(2π)>0, so this unique feasible stationary point is the global minimum. The remaining length is 28π/(π+4).
Master Chapter 6: Applications Of Derivatives
Practise interactive questions, flashcards, visual mind maps, and timed board tests for Applications Of Derivatives.
← Previous Question
For a closed cylindrical can of volume 100 cm³, find dimensions…
Next Question →Prove the largest cone inscribed in a sphere of radius R has volume…
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.