Question

Fans the slope of the curve at the indicated point.

Answer 1

Calculate the derivative.

Answer 2

\[
\frac{d}{dx}|x| =\begin{cases}
\frac{d}{dx}( x)& x>0\\
\frac{d}{dx} (-x)&x<0
\end{cases} =\begin{cases}
1& x>0\\
-1&x<0
\end{cases}
\]You can now use chain rule.

Answer 3

\[
u = x-2\quad \frac{du}{dx}=1
\]Thus \[
\frac{d}{dx}|x-2| = \frac{d}{dx}|u|\cdot 1 = \begin{cases}
1 &u>0\\
-1&u<0
\end{cases}= \begin{cases}
1 &x-2>0\\
-1&x-2<0
\end{cases}= \begin{cases}
1 &x>2\\
-1&x<2
\end{cases}
\]

Answer 4

Final step click this -------------------------------------------->

Answer 5

cool :)