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NCERT Class 12 · Ch 6 Exercise 6.1 · Q10

NCERT Class 12 Maths · Chapter 6 Applications Of Derivatives · Exercise 6.1 Question 10

A 5 m ladder leans against a wall. Its foot moves away at 2 cm/s. Find the height-decrease rate when the foot is 4 m from the wall.
Ladder: exact 3–4–5 right triangle
Ladder: exact 3–4–5 right triangle

💡 Concept Hints

  1. Identify the domain and the inner and outer functions, or the relevant one-sided limits.
  2. Apply the appropriate differentiation or limit rule, keep all chain factors, and check exceptional points.

✅ Step-by-Step Solution

Final Answer: Height rate −8/3 cm/s; decreasing at 8/3 cm/s.
  1. Use metres consistently: xₜ=0.02 m/s. The fixed ladder gives x²+y²=25; at x=4, y=3 m.
  2. Differentiate: 2xxₜ+2yyₜ=0, so yₜ=−(x/y)xₜ=−(4/3)·0.02=−2/75 m/s.
  3. Convert to centimetres: yₜ=−8/3 cm/s.

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