Question

Let \( f_n(x) \) be the \(n^{\text{th}}\) derivative of \( f(x) \). The least value of \( n \) such that \[ f_n(x) = f_{n+1}(x) \] where \[ f(x) = x^2 + e^x \] is: 

• A. 4
• B. 5
• C. 2
• D. 3
• E. 6

Hint:

For any function \( f(x) = P(x) + e^{x} \) where \( P(x) \) is a polynomial of degree \( k \), the condition \( f_{n} = f_{n+1} \) will first be satisfied when \( n = k + 1 \).

Answer 1

The Correct Option is D