CK-12 Foundation
Derivatives of Trigonometric Functions: Derivative of sin(x)
Graphically find the derivative of sin(x). Using the interactive, pupils graph the slope of the tangent line to the sine function. Class members use the resulting graph to determine the derivative of the sine function. They verify their...
CK-12 Foundation
Logarithmic Differentiation: Graphing the Derivative of a Logarithm
Log the values of the derivative of a logarithm. The interactive plots the derivative of the natural logarithm. Learners first determine the derivative of natural logarithm and the general logarithm. Using the formulas for the...
CK-12 Foundation
Derivatives with Mean Value Theorem and Rolle's Theorem: Maxima and Minima
Rolle with the mean values and derivatives. Scholars complete the statements of Rolle's Theorem and the Mean Value Theorem. Using the interactive to illustrate scenarios, pupils respond to questions concerning the theorems in terms of...
CK-12 Foundation
Higher Order Derivatives—Acceleration and Jerk
Accelerate your class through finding the second derivative. Using a bank of equations, pupils determine the equations for distance, velocity, and acceleration and their associated function notations. With the equations, learners answer...
CK-12 Foundation
Constant, Identity, and Power Rules: Power Rule
Learn to gain power in finding derivatives. The resource introduces the power rule. Using the sliders in the interactive, pupils create polynomial functions and find their derivatives. Given the derivative of a polynomial, learners...
CK-12 Foundation
Antiderivative: Piecing it Together
Build a function backwards. Given a graph of the derivative of a function, pupils piece together a graph of the original function, the antiderivative. Learners use their graphs and the graphs of the derivatives to answer questions about...
CK-12 Foundation
Chain Rule
Keep it on the chains. Pupils work through the steps in the chain rule using the interactive as a guide. Learners identify the two composed functions and their associated derivatives from a set of choices. They continue on to build the...
CK-12 Foundation
Slope of a Tangent Line: Slope of the Tangent and Secant Lines
Learn to find the slope through a single point. The interactive provides a visualization of how to find the slope of a tangent line. With the aid of the visualization, pupils see the definition of the derivative in action. Class members...
CK-12 Foundation
Tangent Line Approximation: Estimating Square Roots
Estimating a square root is as easy as evaluating a linear equation. Using the derivative of the square root function, pupils calculate an estimation of square roots. Class members determine the equation of the tangent line at the value...
CK-12 Foundation
Average and Instantaneous Rates of Change
How can you determine the rate of change on a curve? Pupils use the interactive to discover what happens with the average rate of change as the point move closer to the other. Using the definition of the derivative, learners find that it...
CK-12 Foundation
Related Rates of Car Speeds
Speed up your pupils' understanding of derivatives. Two cars travel in perpendicular distances to each other. With the aid of the interactive, learners visualize the situation. Pupils use the derivative to calculate the instantaneous...
CK-12 Foundation
Absolute Versus Local Extrema
Get the class to take an extreme look at functions. The interactive presents a function on a closed interval with a movable tangent line. Using the given function, pupils determine the extrema, critical points, and points of inflection.
CK-12 Foundation
Absolute Extrema and Optimization: Building the Biggest Box
Optimally, you want the largest box. Given a square piece of box material, pupils determine the size of congruent squares to cut out of the corners to create a box with the greatest volume. Learners determine the equation of the volume...