Determine the slope of $g(x)$ at $x= -1, x= -0.5, x= -0.1, x= -0.01$, and $x= -0.001$, given the piecewise function

$$g(x) = \begin{cases} -x, & \text{if $x<0$} \\ x-x^2, & \text{if $x≥0$} \end{cases}$$ `

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closed as off-topic by amWhy, Deepesh Meena, Shailesh, Strants, José Carlos Santos Sep 14 at 16:30

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    Any thoughts? Perhaps if you sketched the graph of $g(x)$ it would be clearer to you. – lulu Sep 14 at 12:56


$$g'(x) = \begin{cases} -1, & \text{if $x<0$} \\ 1-2x, & \text{if $x≥0$} \end{cases}$$

Here you want to find slope only when $x$ is negative in every case.

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