COMEDK · Maths · 27. Application of Derivatives
The least value of ' \(a\) ' such that the function \(x^2+a x+1\) is increasing on \([1,2]\) is
- A \(1\)
- B \(4\)
- C \(-2\)
- D \(2\)
Answer & Solution
Correct Answer
(C) \(-2\)
Step-by-step Solution
Detailed explanation
Let \(f(x) = x^2 + ax + 1\). The function \(f(x)\) is increasing on the interval \([1, 2]\) if its derivative \(f'(x) \ge 0\) for all \(x \in [1, 2]\). Calculating the derivative, we get \(f'(x) = 2x + a\). For \(f(x)\) to be increasing on \([1, 2]\), we require \(2x + a \ge 0\)…
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