In this activity, students will observe the slopes of the secant and tangent line as a point on the function approaches the point of tangency.

Students learn how to find and label extrema using first and second derivatives, be able to inspect a graph and determine which extrema the function has, and be able to use trace, fMin, and fMax to verify the computed answers and find critical values for parametric functions.

In this activity, students will explore the behavior of various functions by zooming in on their graphs. They will investigate the concept of local linearity.

Students identify whether a slope field approximately reflects a differential equation. They also determine whether a potential solution fits the slope field.

In this activity, students learn what a slope field represents in terms of dy/dx. Students create a slope field for a given differential equation

In this activity, students will investigate the derivatives of sine, cosine, natural log, and natural exponential functions by examining the symmetric difference quotient at many points. They develop the idea of the derivative as a function. They gather evidence toward some common derivative formulas. They also use numerical and graphical investigations to form conjectures.

In this activity, students explore information about a graph based on the first and second derivatives. They learn that a function's derivative is positive when the function increases and negative when the function decreases. They learn that the second derivative is positive when the graph is concave upward and negative when the graph is concave downward.

Student examine the ascent stage of a NASA space shuttle.