Higher-Order Derivatives and Linear Approximation
Using the Tangent Line Approximation Formula
Tangent Line Approximation / Linearization
Use a linear approximation to approximate the valve of each of the following:
Basic idea of Newton's Method and how to use it.
One example using Newton's Method to approximate a root.
Find where f(x) = x7
- 1000 intersects the x-axis; find solution correct to 8 decimal places.
Compute two iterations of Newton's method for the given function and indicated initial guess:
f(x) = x2
- 8, x1
Apply two iterations of Newton's method to approximate the x-value of a point of intersection of these two functions using the given initial guess:
f(x) = x2
- 4, g(x) = 2x - 3, x1
What is the value of x3
Newton's Method - How it Can FAIL
Given the following equation and initial guess, why would Newton's method fail to approximate a solution?
f(x) = (x - 2)2
- 1; x1
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