Limits and Riemann sums
One scale shrinks both the area slices and the local step, and the definite integral and the derivative both come out of a finite approximation.
Derivatives and tangent lines
5 pieces about this concept, across works, topic guides, and exam visualizations.
Topics
Works
Tangent approximation
The secant slope approaches the tangent slope, so the derivative reads as an instantaneous rate of change.
Taylor polynomial approximation
Change the degree n and the center a, and watch the Taylor polynomial fit sin x, cos x, and e^x locally.
A function and its derivative
Compare f(x) with f'(x), and watch increase, extrema, and the tangent slope move together.
Gradient and level curves
Drag a point in the plane and watch the gradient stay orthogonal to the level curve, pointing where the function increases fastest.