Mitchell J. answered • 04/04/21
Dartmouth grad, Current math PhD student with 7+ years experience
To solve this, you take the fourth derivative of the Maclaurin series for f(x). For each derivative, the only non-zero component in the sum is the constant since it is being evaluated at x=0. Therefore, to evaluate the fourth derivative, we only need to consider the fourth derivative of the x^4 term, since the fourth derivative of any higher terms would still have x's in them, thus making them zero when evaluated at x=0, and the fourth derivative of lower terms would just be zero since we would be at some stage taking the derivative of a constant. Thus the fourth derivative of f(x) would be 4! * c_4 if c_4 is the constant in front of the x^4 term. Without seeing this constant, we cannot solve this question however.
