Learn how calculus finds the “turning points” of a curve — where a function reaches a local maximum, local minimum, or changes direction. This video shows how critical points and the first derivative test let us understand the shape and behavior of a graph without plotting every point.
ATP: The Curve Behind Every Movement — a story about how a biological curve can be studied using the same ideas as motion graphs. ATP is the tiny energy molecule that powers every movement in your body — from running and jumping to simply breathing. In this story, you will see how the rise and fall of ATP can be studied using the same calculus ideas we use for motion graphs, critical points, and curves.
x², −x², x³, −x³. Compute f, f′, f″ values and identify max/min/inflection.A(t) and V(t) and draw the curve for D(t) based on the these and where the derivatives change signs (without finding many point for drawing full curves for D(t)).A(t) and V(t) and draw the curve for D(t) based on the these and where the derivatives change signs (without finding many point for drawing full curves for D(t)).