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

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

3. 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)

4. 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).

5. 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

6. Homework:
Worksheet Provided
NOT SUGGESTED!