Start from slope on the graph itself, then widen into signed area and accumulation so rate and total change stay connected on one visual branch.
This first calculus page stays on an honest graphing bench instead of splitting slope and integral ideas too early. Derivative as Slope / Local Rate of Change keeps the moving point, tangent line, secant line, and derivative graph linked so local steepness never drifts into detached notation, and Integral as Accumulation / Area keeps the same graph-first language while the running total grows from signed area.
Best first concepts
The topic page keeps these starts in their own compact row so the first screen is about orientation and next action, not stacked feature cards.
Slide a point along one curve, tighten a secant into a tangent, and connect local steepness to the derivative graph without leaving the same live bench.
Tangent and local change
Strong first stop for getting into this topic without scanning the whole library.
Move one upper bound across a source curve and watch signed area build into a running total so accumulation stays visual instead of symbolic.
Accumulation and area
Strong first stop for getting into this topic without scanning the whole library.
Related guided tracks
These tracks stay tied to the same shared concept pages and progress model. They are surfaced here either because the authored path meaningfully overlaps this topic page or because the topic catalog marks the track as useful preparation for this branch.
Keep the first math path compact: read parent-curve moves first, then local slope, and then accumulation so change stays graph-first all the way through.
Track progress
0 / 5 moments complete
0 / 3 concepts and 0 / 2 checkpoints cleared.
Graph Transformations opens this track and sets up the rest of the path.
Specific learning goals
These goal cards stay authored and transparent. They reuse the current topic page, starter tracks, guided collections, concept bundles, and progress cues instead of adding a separate recommendation system on top of this branch.
Use the functions topic route, the compact math starter track, and the calculus topic route so graph moves, local slope, and accumulation stay on one coherent bench.
Primary move
Open topic route
No saved progress yet inside Functions.
Entry diagnostic
Start from beginning
No saved diagnostic checks are available yet, so the opening concept is still the best place to start.
Reuses the starter track entry for Functions and Change, with 0 of 2 probes already ready.
No saved progress yet inside Functions.
Graph Transformations opens this track and sets up the rest of the path.
No saved progress yet inside Calculus.
Grouped concept overview
Each group is authored in the topic catalog, but the actual concepts, progress badges, and track cues still come from the canonical concept metadata and shared progress model.
Group 01
Keep one curve in view while the secant line collapses into the tangent, then let signed area build a running total so local rate and accumulation stay linked on the same branch.
Slide a point along one curve, tighten a secant into a tangent, and connect local steepness to the derivative graph without leaving the same live bench.
Strong first stop for getting into this topic without scanning the whole library.
Move one upper bound across a source curve and watch signed area build into a running total so accumulation stays visual instead of symbolic.
Strong first stop for getting into this topic without scanning the whole library.