CPM Homework Help : CALC Problem 3-122

Find all values of $x$ where $f^\prime(x) = 2$ given $f ( x ) = \frac { 1 } { 3 } x ^ { 3 } - \frac { 5 } { 2 } x ^ { 2 } - 4 x + 13$ .

Hint:

Since $f(x)$ is cubic, $f^\prime(x)$ will be quadratic. Predict how many solutions there will be to $f^\prime(x) = 2$ .

Answer:

The blue curve shows $f^\prime(x)$ intersecting the dotted line $y = 2$ . Do your solutions look correct?

Step 1:

Use the Power rule to find $f^\prime(x)$ .

Step 2:

Set $f^\prime(x) = 2$ , and solve for $x$ .

Use the eTool below to explore the graph of $f(x)$ .
Click the link at right for the full version of the eTool: Calc 3-122 HW eTool