The slope of the tangent line is the first derivative . Find the two points where the slope is exactly zero.
Points where can be Local Extrema. Tap the highest point (local max) and lowest point (local min) in the region.
The second derivative tells us about concavity. Positive = Smile 😃, Negative = Frown 😞. Drag to find where the curve changes its mood!
Drag the curve segments to the boxes that match their derivative signs.
You've successfully analyzed functions using the first and second derivatives to find critical points, extrema, and concavity.