Doubly Tangent LineCalculus Level pending
Let the quartic function \( f(x) \) be given by
\[ f(x) = x^4 - 8 x^3 +17 x^2+ 2x - 24 \]
Then, there is a unique line that is simultaneously tangent to the graph of \( f(x) \) at two distinct points. Let this line be described by
\[ y = m x + b \]
Find \( m + b \).