Unit 13: The slope of the slope
About this unit
The second derivative is the rate at which the slope changes: acceleration for motion, and for a graph it says which way the curve bends.
By the end, you can: Read the second derivative as how fast the slope changes: acceleration in motion, which way a graph bends, inflection points and the second-derivative test.
Modules
5 modulesLearn
- Rates of ratesArticle · Differentiate twice: position, velocity, acceleration for a braking car s = 20t − 2t²; then the third derivative, jerk.Not started
- Which way the graph bendsArticle · f″ > 0 means the slope is rising and the graph cups upward; f″ < 0, it bends down; f″ changing sign marks an inflection point; f″ classifies flat points.Not started
- Hunt for the steepest descentExperiment · Drag along x³ − 3x to where its slope is lowest (−3 at x = 0) and see that this is where the bending flips.Not started
- Second derivatives in briefReview · f″ is the slope's rate of change: acceleration, concavity, inflection points, the second-derivative test, and its limits.Not started