ANSWER
[tex]\begin{equation*} -8 \end{equation*}[/tex]
EXPLANATION
To find the slope of the function at the given point, we have to apply the formula:
[tex]slope=\lim_{h\to0}\frac{f(a+h)-f(a)}{h}[/tex]
where a = x-coordinate of the point.
From the question, a = 2.
Therefore, the slope of the function at x = 2 is:
[tex]\begin{gathered} slope=\lim_{h\to0}\frac{2(2+h-4)^2-2(2-4)^2}{h} \\ \\ slope=\lim_{h\to0}\frac{2(h-2)^2-2(-2)^2}{h}=\lim_{h\to0}\frac{2(h^2-4h+4)-8}{h} \\ \\ slope=\lim_{h\to0}\frac{2h^2-8h+8-8}{h}=\lim_{h\to0}\frac{2h^2-8h}{h} \\ \\ slope=\lim_{h\to0}2h-8=0-8 \\ \\ slope=-8 \end{gathered}[/tex]
That is the slope at the given point.
