Answer
$20$
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
$f'(x) =\lim\limits_{x \to c} \dfrac{f(x)-f(c)}{x-c}$
We plug in the given equation $f(x)=2x^3-x^2$ at $x=2$:
$f'(2)= \lim_{x\to 2}\limits\dfrac{f(x)-f(2)}{x-2}\\=\lim_{x\to 2}\dfrac{2x^3-x^2-(2(2)^3-(2)^2)}{x-2}\\=\lim_{x\to 2}\limits\dfrac{2x^3-x^2-12}{x-2}\\=\lim_{x\to 2}\limits\dfrac{(x-2)(2x^2+3x+6)}{(x-2)}
\\=\lim_{x\to 2}\limits2x^2+3x+6\\=2(2)^2+3(2)+6 \\=20$
