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

4-38.

Sketch a graph of .

Calculate the slope of the line tangent to the curve at

.Recall that the slope of the tangent line at

is also known as.Determine the point on the curve where the slope is the smallest (steepest negative slope). What is the name of this point?

You are looking for the location where

is at its lowest (or at a minimum). To find this location, you will need to find the location (-value) of the lowest point (the vertex) on the graph ofNote:. is a parabola, so an Algebra I student could complete this part of the task.Use the

-value of the vertex of, to evaluate the coordinate point onwhere the slope is the steepest.