### Home > APCALC > Chapter 3 > Lesson 3.4.3 > Problem3-174

3-174.

Sketch the graph of $f(x) = x(x − 1)$, and use the graph to sketch the graph of the slope function.).

$f(x)$ is a parabola, so $f ^\prime (x)$ will be linear.

Notice the negative slope when $x < 0.5$. This means the graph of $f ^\prime (x)$ will have negative values on this domain.

Notice the positive slope when $x > 0.5$. This means the graph of $f ^\prime (x)$ will have positive values on this domain.

Notice that $x = 0.5$ is the $x$-value of the local minimum. This means the graph of $f ^\prime (x)$ will have a root at $x = 0.5$.

Use the eTool below to visualize this problem.
Click the link at right for the full version of the eTool: Calc 3-174 HW eTool