### Home > APCALC > Chapter 3 > Lesson 3.3.3 > Problem3-122

3-122.

Determine all values of $x$ where $f^\prime (x) = 2$ given $f(x) = \frac{1}{3}x^3 − \frac{5}{2}x^2 − 4x + 13$ . 3-122 HW eTool (Desmos) Homework Help ✎

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

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

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

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

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