Question

inding the Slope of a Graph, find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results.

Answer 1

`\begin{equation*} -8 \end{equation*}`

Step-by-step explanation

To find the slope of the function at the given point, we have to apply the formula:

`slope=\lim_(h\to0)(f(a+h)-f(a))/(h)`

where a = x-coordinate of the point.

From the question, a = 2.

Therefore, the slope of the function at x = 2 is:

`\begin{gathered} slope=\lim_(h\to0)(2(2+h-4)^2-2(2-4)^2)/(h) \\ \\ slope=\lim_(h\to0)(2(h-2)^2-2(-2)^2)/(h)=\lim_(h\to0)(2(h^2-4h+4)-8)/(h) \\ \\ slope=\lim_(h\to0)(2h^2-8h+8-8)/(h)=\lim_(h\to0)(2h^2-8h)/(h) \\ \\ slope=\lim_(h\to0)2h-8=0-8 \\ \\ slope=-8 \end{gathered}`

That is the slope at the given point.