1. 3.9 Linear Approximations

2. b) Then use it to approximate the following:
Ex 1: a) Find the linearization of f(x) at x = 1.
b) Then use it to approximate the following:

3. Ex 1:
c) For what values of x is the linear approximation accurate to within 0.5?

4. 3.9 Differentials
Differential:

5. dy represents the amount that the tangent line rises/falls.
y represents the amount that the curve (i.e. secant line) rises/falls.

6. Q dy y P
dx = x x
x + x

7. Compare the values of y and dy if
Ex 2:
Compare the values of y and dy if
y = f(x) = x3 + x2 –2x + 1 and x changes from 2 to 2.05.

8. HW – 3.9 pg. 240 # 1 – 25 odds, # 43 – 47 odds

9. Read Apps to Physics
pg. 262

10. Ex 2: Suppose that after stuffing a turkey its temp is 50° F & you put it in a 325° F oven. After 1 hr. the turkey is 93° F & after 2 hrs. the turkey is 129° F. Predict the temp after 3 hrs.