Doubly Tangent Line

Calculus 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 \( m + b \).

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