NCERT Class 12 · Ch 6 Exercise 6.3 · Q11
NCERT Class 12 Maths · Chapter 6 Applications Of Derivatives · Exercise 6.3 Question 11
x⁴−62x²+ax+9 attains its maximum on [0,2] at x=1. Find a.
💡 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: a=120.
- The maximum is at an interior differentiable point, so f′(1)=0. Since f′=4x³−124x+a, 4−124+a=0 gives a=120.
- With that value, f′=4(x−1)(x²+x−30). The quadratic factor is negative on [0,2], so f increases to 1 and decreases after it. This verifies the maximum condition.
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