Section 3.9 Linear Approximation and the Derivative.

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Presentation transcript:

Section 3.9 Linear Approximation and the Derivative

Recall that when we “zoomed in” on a differentiable graph, it became almost linear, no matter how much curve there was in the original graph Therefore a tangent line at x = a can be a good approximation for a function near a Let’s take a look at the function and its tangent line at x = 0

Between -.1 and.1 both graphs look almost identical Let’s find the tangent line at x = 0 and use it to find f(-.5), f(-.1), f(.1), f(.5), and f(1) We will then compare these to their actual function values

Estimating the error in linear approximations The error in using a tangent line approximation (near x = a) is given by This is explored further in Taylor polynomials in chapter 10 Let’s find the approximate errors for our estimations and see how they compare to the actual