Calculus Visual Tools

12Tools

5Categories

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4 tools · 1 sub-group

Calculus

Derivatives4 tools

Average Rate of Change Visualizer

Drag two sample points along the cubic curve f(x) = ⅓x³ − x to watch the secant slope Δy/Δx update in real time. Four animated scenarios — ascending, descending, local max, and local min — walk through the geometry that turns the average rate of change into the derivative, with synchronized computation, meaning, and theory panels.

Inflection Points and Concavity Visualizer

Drag point c along the cubic f(x) = (1/3)x^3 - x to see how the sign of f''(c) decides whether the curve is concave up, concave down, or inflecting. Three pre-built scenarios animate the seven analysis steps from picking a region to evaluating f''(c) and shading the concavity gap between curve and tangent.

Newtons Method Visualizer

Drag a starting guess x₀ along the x-axis for f(x) = x³ − 2x − 5 and watch each Newton step draw its tangent, drop to the x-axis, and lift back to the curve. Three preset scenarios show a direct hit, a slow crossover, and a stalling failure when x₀ lands near a critical point where the tangent goes nearly horizontal.

Tangent Line Visualizer at a Point

Drag point c along the cubic f(x) = (1/3)x^3 - x to see the tangent line drawn through P = (c, f(c)) with slope f'(c). Four pre-built scenarios animate the six analysis steps for positive slopes, negative slopes, local maxima, and local minima, then write the tangent in point-slope form.

2 tools

Limits and Continuity

Continuity Checker

Probe continuity at any point with a live three-condition checklist — f(c) defined, two-sided limit exists, f(c) equals the limit. Slide c through holes, jumps, asymptotes, and staircases and watch each row flip pass or fail in real time.

Limit Explorer

Watch left and right limits race toward each other as epsilon shrinks. Switch between seven canonical cases — continuous, hole, jump, infinite asymptote, oscillating, and one-sided — and read the verdict for both the limit and the continuity at c.

3 tools

Derivatives

Derivative Visualizer

Move x0 along the graph and watch three pictures of one number lock together — the slope of the tangent on f, the height of f-prime at x0, and the numeric derivative value. Snap directly to roots, extrema, and inflection points to see why each one matters.

Mean Value Theorem Visualizer

Draw a secant between any two points on a smooth curve and the tool finds every interior c where the tangent has matching slope — the parallel-tangent guarantee at the heart of the Mean Value Theorem. Six function families illustrate the single-c, multi-c, and exact-midpoint cases.

Optimization Visualizer

Find every critical point of a smooth function on a chosen interval and watch the second-derivative test classify each as local max, local min, or inflection. Six families show single-extremum cases, W-shapes, and touch zeros where the test falls back to the first-derivative test.

1 tool

Diagrams

Calculus Diagrams

A gallery of every diagram already shown on the calculus pages: figures drawn for the lessons and frozen states of the visual tools. Browse by chapter or page, search captions, compare two figures side by side, and jump from any picture to the exact section where it appears or to the tool that drew it.

2 tools

Integrals

Fundamental Theorem of Calculus Visualizer

See both halves of the Fundamental Theorem of Calculus on one graph — slide x to grow the shaded area under f and watch the accumulator F match the area exactly, while the slope of F at every x equals f at the same point.

Riemann Sum Visualizer

Approximate a definite integral with rectangles or trapezoids, then watch the error shrink as you increase the partition count. Switch between left, right, midpoint, and trapezoid rules to see why some converge as one over n and others as one over n squared.