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...
Corbett Maths
Instantaneous Rates of Change
Here's a great lesson that looks at slope as an instantaneous change. Using an estimated tangent line, the presenter shows the class how to find an approximation for the instantaneous rate of change. Scholars determine the slope of the...
College Board
Approximation
Sometimes close enough is appropriate. A curriculum document for AP® Calculus examines the importance of providing approximation questions throughout the course. It looks at approximating derivative values, approximating definite...
Curated OER
Secant Line Approximation of the Tangent Line
Students perform operation with secant and tangent lines. In this calculus lesson, students find the derivative and relate it to the slope of a line. They differentiate between secant and tangent as they intersect a circle, using Cabri.
Curated OER
Taylor's Theorem and Error in Tangent Line Approximations
In this tangent line approximation worksheet, students answer two essay questions about the approximation error when related to a function. They answer three short answer problems. Students graph one function and its tangent line.
Curated OER
Local Linearity and the Microscope Approximation
In this local linearity worksheet, students identify the slope of a line tangent to the graph at a given point. They use linear approximation to estimate values. Students determine the slope of a secant line at a given point. This...
Curated OER
Center of Mass, Tangent Line Error Bound
In this center of mass worksheet, students determine the center of mass of an isosceles triangle. They examine functions and determine the tangent error bound. This one-page worksheet contains 5 problems.
Curated OER
Higher Order Taylor Polynomials
In this polynomial worksheet, students approximate values of linearly using the tangent line. They use first and second-degree polynomials to find the equation of a line tangent to a graph. Students explore Taylor's Theorem. This...
CK-12 Foundation
Newton's Method
Use an iterative process to find an approximation of a square root. Pupils use the interactive to find an approximation to find the positive root of a quadratic function with Newton's method. With the graphs, learners position the...
Flipped Math
Calculus AB/BC - Estimating Derivatives of a Function at a Point
It seems like it should be about three. Pupils learn to get an estimate of the derivative of a function at a point by using the derivative functionality of their graphing calculators. They take that information to determine the equation...
Curated OER
Differentiability and Linear Approximation
In this linear approximation worksheet, students determine the derivative of a function and explore properties of the error when using a tangent line to approximate a function graph. This two-page worksheet contains four problems.
Curated OER
Differentiability and Linear Approximation
In this differentiability worksheet, students write expressions for a tangent line approximation to a graph, determine the limits, and use Taylor's theorem to differentiate given functions. This three-page worksheet contains a...
Curated OER
Three Calculus Overview Problems
In this calculus overview worksheet, students: find the equation of a tangent line, curve sketch, and find limits. Students should have covered continuity as well.
Curated OER
Implicit Differentiation
In this implicit differentiation instructional activity, students use the chain rule to solve for the derivative. The find the equation for the tangent line at a given point and determine if the line is vertical. This two-page...
Curated OER
Geometry Course Review
For this geometry review set of worksheet, 10th graders solve and complete 139 various types of problems. First, they find the slope-intercept form of a line passing through a point and parallel to a line given. Then, students find the...
Curated OER
Newton's Method
Student approximate the roots of E using Newtons Method. In this calculus lesson, students calculate the equation of tangent a line. They use the TI to visualize the tangent line.
Curated OER
Limits and Trigonometric Equations.
In this calculus instructional activity, students solve functions dealing with limits and the 6 trigonometric values. They find the slope and tangent lines. There are 28 questions.
Curated OER
Math 155 - Fall 2005 Differentiation
In this differentiation worksheet, students find an equation of a line tangent to a curve. They use linear approximation to estimate answers. This two-page worksheet contains approximately 12 multi-step problems.
Curated OER
Taylor's Theorem
In this Taylor's Theorem learning exercise, students use the microscope approximation to determine the approximate value of a function. They rewrite expressions for the relative error, and observe changes in the relative error. They...
Mathematics Assessment Project
College and Career Readiness Mathematics Test C2
Scholars apply knowledge learned over their high school math courses in order to determine their college readiness. The 20-page resource emphasizes applied problem solving.
Curated OER
A.P. Calculus Exam Prep
In this A.P. Calculus exam practice test, students answer 28 multiple choice questions. Questions cover a wide variety of topics. Students tell the position of a particle moving along a horizontal line. They identify the solution to a...
Kenan Fellows
Man vs. Beast: Approximating Derivatives using Human and Animal Movement
What does dropping a ball look like as a graph? An engaging activity asks learners to record a video of dropping a ball and uploading the video to software for analysis. They compare the position of the ball to time and calculate the...
Curated OER
The Definition Derivative
In this derivative learning exercise, students evaluate limits, factor equations, and calculate the given function. They determine the derivative of a function and plot it on a graph. This four-page learning exercise contains eight...
Curated OER
Worksheet 14
In this math worksheet, students graph the function f(x) = sinx on a set of axes that is at least half the size of a page of notebook paper.