Section 3.9 Linear Approximation.

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Presentation transcript:

Section 3.9 Linear Approximation

Linear Approximation A way to use derivatives to approximate nonlinear functions by simpler linear functions.

A Graph & Its Tangent Think about the value at x = a of f(x) and of the tangent line. We can use the tangent line as an approximation to the function f(x) near x = a. In these cases we call the tangent line the linear approximation to the function at x = a.

Ex: Use a linear approximation to find What function would be helpful to use in this case?

Ex: Use a linear approximation to find Step 1: Choose a function we can calculate easily… Let f(x) = ________ at x=____. Step 2: Graph f and show tangent line at x = ____. Step 3: Find the equation of the tangent line to f(x) at the point you chose. Point: ( , ) Slope: m = ______ Tangent Line Equation: Step 4: Put in 3.9 for the x-value in the tangent line equation to estimate. Is this an under or over approximation? Hint: Is the line you used above or below f(x)?

Ex: Use a tangent line approximation to approximate the following B)

Ex: Use a linear approximation to find Is this on over or under approximation?

Food for thought: Why isn’t our approximation as accurate as the calculator? How could we possibly get a more accurate approximation? How do you think the calculators are programmed to approximate? Where might linear approximation be used in the real world?

Homework Linearization worksheet Work on Practice Test You will have time to work on this next week, but I will not be here on Wednesday and Thursday. I would suggest taking a look at the practice test this weekend so we can talk about your questions on Monday. Monday will be the only day for tutoring next week.