NCERT Class 12 · Ch 6 Exercise 6.1 · Q11
NCERT Class 12 Maths · Chapter 6 Applications Of Derivatives · Exercise 6.1 Question 11
A particle moves on 6y=x³+2. Find points where the y-coordinate changes eight times as fast as x.
💡 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: (4,11) and (−4,−31/3), for a nonzero instantaneous x-rate.
- Differentiate in time: 6yₜ=3x²xₜ, so yₜ/xₜ=x²/2 when xₜ≠0.
- Set x²/2=8 to get x=±4.
- At x=4, y=(64+2)/6=11; at x=−4, y=(−64+2)/6=−31/3.
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