Step {{ step }} / {{ totalSteps }}

Drag to find flat spots!

The slope of the tangent line is the first derivative . Find the two points where the slope is exactly zero.

x = -2 x = {{ s1.x.toFixed(2) }} x = 2
First
Second

Tap the peaks and valleys!

Points where can be Local Extrema. Tap the highest point (local max) and lowest point (local min) in the region.

Local Max
Local Min

Find the Inflection Point!

The second derivative tells us about concavity. Positive = Smile 😃, Negative = Frown 😞. Drag to find where the curve changes its mood!

{{ s3.emoji }}
x = -2
x = {{ s3.x.toFixed(2) }}
x = 4

Build the Graph!

Drag the curve segments to the boxes that match their derivative signs.

All pieces placed!
🏆

Calculus Mastered!

You've successfully analyzed functions using the first and second derivatives to find critical points, extrema, and concavity.

  • Found roots of
  • Identified Local Extrema
  • Discovered Inflection Points
  • Reconstructed curve shapes