Warm up Problems 1. If y – 5x 10 – ln(xy) = 2 sin x, find 2. Find the equation of the line tangent to x 3 + y 3 = 6xy at (3,3).

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Presentation transcript:

Warm up Problems 1. If y – 5x 10 – ln(xy) = 2 sin x, find 2. Find the equation of the line tangent to x 3 + y 3 = 6xy at (3,3).

After correcting the homework, we will be taking Derivative Quiz #2.

Linear Approximation We can use the tangent line to approximate the value of a function at a difficult point. Here’s a demo.Here’s a demo.

 This is just the equation of the tangent line. Called linear approximation, tangent line approximation, or local linearization. near x = a

Ex. Find the local linearization of near x = 1.

Ex. Find the linear approx. of near x = 3, then use it to approx. f (3.04) and f (2.97).

Ex. Estimate. Is this estimate higher or lower than the actual value?

Next class we will review, and our chapter test will be on Monday.