Prime equals triple prime?
Calculus
Level
3
For some infinitely differentiable function \(f(x) \), it satisfies the above equation. Given the initial conditions
\[ f(1) = 6, f'(1) = 5, f''(1) = -3 \]
What is the value of \( f( \ln(42) ) \)?
Details and Assumptions
\( f'(k), f''(k), f'''(k) \) denote the first, second, and third derivative of \(f(x) \) at \(x=k\) respectively.
Image Credit: Wikimedia Taylor Series
by
Caleb Townsend