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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