Linear Approximations AP Calculus BC February 21, 2018 Mrs. Agnew

Essential Stuff Essential Question Essential Vocabulary What are linear approximations? Essential Vocabulary Linearization Linear Approximation Tangent Line

Linear Approximations Recall that the tangent line to a function at the point ( a, f(a) ) is given by f(x) – f(a) = f’(a) (x – a) Therefore, the linear approximation of f at x = a is given by f(x) ≈ f’(a) (x – a) + f(a)

Linear Approximations The linear approximation is a good approximation for the function when x is near a. In other words, we can estimate function values by plugging x into the linear approximation (as long as x is near a).

Guided Practice Use the linearization of at a = 1 to approximate the values of and Are your approximations overestimates or underestimates? Why??? Linear Approximation Worksheet

Homework: Worksheet Provided NOT SUGGESTED!