### Home > CALC > Chapter 4 > Lesson 4.1.3 > Problem 4-38

4-38.

Recall that the slope of the tangent line at *x* = *a* is also known as *f* '(*a*).

You are looking for the location where *f* '(*x*) is at its lowest (or at a minimum). To find this location, you will need to find the location (*x*-value) of the lowest point (the vertex) on the graph of *f* '(*x*). Note: *f* '(*x*) is a parabola, so an Algebra I student could complete this part of the task.

Use the *x*-value of the vertex of *f* '(*x*), to evaluate the coordinate point on *f*(*x*) where the slope is the steepest.