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 of . Note: is a parabola, so an Algebra I student could complete this part of the task.
-value of the vertex of , to evaluate the coordinate point on where the slope is the steepest.