### Home > CALC > Chapter Ch3 > Lesson 3.4.3 > Problem 3-174

3-174.

*f*(*x*) is a parabola,so *f* '(*x*) will be linear.

Notice the negative slope when *x* < 0.5. This means the graph of *f* '(*x*) will have negative values on this domain.

Notice the positive slope when *x* > 0.5. This means the graph of *f* '(*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* '(*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