CPM Homework Help : CALC Problem 3-174

Sketch the graph of $f(x) = x(x-1)$ , and use this graph to sketch the graph of the slope function, $f^\prime(x)$ .

Hint 1:

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

Hint 2:

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

Hint 3:

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

Hint 4:

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