Question

Let \(f(x) = -x^3 + 9x^2 - \alpha x - 13\), where \(x \in \mathbb{R}\) and \(\alpha\) is a constant. If the function \(f\) is increasing only in the interval (1,5), then the value of \(\alpha\) is equal to

• A. 12
• B. 13
• C. 14
• D. 15
• E. 16

Hint:

For a quadratic \(f'(x)\) with roots \(p\) and \(q\), the constant term is usually linked to the product of roots. Always verify if the sum of roots matches the middle coefficient first.

Answer 1

The Correct Option is A