If \(f(5)=1\) and \(f'(5) = 4\), then what is the equation of the tangent line to \(f\) at \(x=5\)? What is the linear approximation of \(f(4)\)?

Equation of the tangent line to \(f\) at \(a=5\):

\[y = 1+\answer {4}\cdot (x-\answer {5})\]
The linear approximation, \(L(x)\), of \(f\) at \(a=5\);
\begin{align*} L(x) &= \answer {1+4(x-5)}\\ f(4) \approx L(4) &= \answer {-3} \end{align*}