Taylor's Theorem and Error in Tangent Line Approximations

Providing both review and practice problems, this worksheet prompts students to answer five questions having to do with slope, tangents lines, graphing, the Squeeze Theorem, differentiable functions and derivatives. This activity could...

Using a specific example, Sal shows how to find the equation of a tangent line to a given function at a specific point. Specifically, he solves the problem of finding the tangent line to the function f(x) = xex at x = 1. This problem...

Given a function and a point on the function, the video shows how to determine the equation of the tangent line at that point. Using the function equation, the presenter determines the y-coordinate for the point. The 24th video in a...

Is it normal to find a perpendicular line to the tangent line? The short video provides a problem to find the equation of the normal line to a function. Beginning with an explanation of the normal line, the 27th installment in a 31-part...

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...

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...

Does the point continually move along the graph? Pupils drag a line across two functions to determine whether they are continuous or not. They answer questions about the properties of continuous and discontinuous functions. Using their...

Is the inverse of a function also a function? Pupils manipulate the graph of a function to view its inverse to answer this question. Using a horizontal and vertical line, class members determine whether the initial function is...

One-to-one means the answer is simple, right? Given four graphs, pupils use a vertical line to test each graph to find out if they are one-to-one. By using the resource, learners realize that not all one-to-one relations are functions....

Provide a graphical view of inverses. Pupils manipulate points on a line and see the relationship of the graph with the graph of its inverse. Using the relationship between the graphs, scholars respond to questions concerning inverses...