Question

If f ' (x) = |x-2|, what is a possible graph of y = f(x)

Answer 1

please draw

Answer 2

\[\large f'(x)=
\begin{cases}
x-2 &\text{if }x\geq2\\
2-x &\text{if }x<2
\end{cases}\\
\large f(x)=
\begin{cases}
\frac{1}{2}x^2-2x+c_1 &\text{if }x\geq 2\\
-\frac{1}{2}x^2+2x+c_2 &\text{if }x<2
\end{cases}\]
where c1 and c2 are arbitrary constants.
You can draw these, right?

Answer 3

So they would have different limits at x=2?

Answer 4

That depends on the constants. What you can do is just pick convenient values for c1 and c2 and draw the graphs accordingly.

Answer 5

Well, since f' is an absolute value equation, it will always be non-negative, and you can see that the slope is 0 when x=2.

Answer 6

Here are my options