NCERT Class 12 · Ch 6 Exercise 6.2 · Q14
NCERT Class 12 Maths · Chapter 6 Applications Of Derivatives · Exercise 6.2 Question 14
For which a is f(x)=x²+ax+1 increasing on [1,2]?
💡 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≥−2.
- f′=2x+a, whose smallest value on [1,2] is 2+a at x=1.
- Requiring it nonnegative gives a≥−2. Equality still gives strict increase since f′>0 for x>1.
- If a<−2, the derivative is negative immediately to the right of 1, so the condition is necessary too.
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