Differentiation Rules and Linear Approximations

These flashcards cover concepts related to differentiation rules, linear approximations, and the application of differentials in estimating errors.

What is the purpose of finding the linear approximation of a function?

To estimate the values of the function near a point using the tangent line.

What are differentials used for in the context of approximations?

To estimate the maximum possible error, relative error, and percentage error in calculations.

What does it mean to find the linearization of a function at a point?

It means approximating the function by a linear function (tangent) at that point.

What factors determine the accuracy of a linear approximation?

The function's behavior and the distance from the approximation point.

In estimating the area of a circular disk, what is the impact of measurement error in the radius?

It leads to discrepancies in the calculated area, which can be estimated using differentials.

What example is given regarding the edge of a cube measurement?

Finding maximum possible error, relative error, and percentage error in computing the volume from a given edge length.

Why is it important to graph the function and its tangent line?

To visually illustrate how well the linear approximation matches the actual function.

What do you need to verify a linear approximation at a point?

The function's derivative at that point and the value of the function.