Answer
$8$
Work Step by Step
Consider the tangent line that contains the point $(x, c)$. The slope the tangent line to the graph of $f(x)$ at $(x, c)$ can be written as
$f'(x) =\lim\limits_{x \to c} \dfrac{f(x)-f(c)}{x-c}$
Consider $c=2$ and $f(x)=3x^2-4x$. Thus, we have:
$f'(2) =\lim\limits_{x \to 2} \dfrac{f(x)-f(2)}{x-2} \\=\lim\limits_{x \to 2} \dfrac{3x^2-4x-4}{x-2} \\=\lim\limits_{x \to 2} \dfrac{(3x+2)(x-2)}{x-2}\\=\lim\limits_{x \to 2} 3x+2\\=8 $
