Let \(f^{(0)}(x) = (1+2x-x^2)^4\), where \(f^{(n)}(x)\) denotes the \(n^\text{th}\) derivative of \(f(x)\). If the value of \(f^{(7)}(0)\) is in the form \(-k!\), where \(k\) is a natural number, find the value of \(k\).

\[\]**Notation:** \(!\) is the factorial notation. For example, \(8! = 1\times2\times3\times\cdots\times8 \).

×

Problem Loading...

Note Loading...

Set Loading...