Linearization Explain in your own words what Linearization is.

Why is Linearization important?

You may not use a calculator on the following. 1) The local linear approximation to the function f at x = -2 is y = 3x – 5. What is the value of f (2)  f '(2) ?

2) Let f be a differentiable function with f (3)  0 and f '(3)  7 . What is the value of the approximation of f (3.2) using the function’s local linear approximation at x = -3?

3) Let h( x)   x  3 . Write an expression to approximate h around x = -2. 2

Newton’s Method Newton's Method

xn+1 = xn -

f  xn  f'  xn 

Explain in your own words what Newton’s Method does and how it works.

4) Approximate the zero(s) of the function using Newton’s method within 0.001. Use an initial guess of x = 1 SHOW ALL WORK!! (You may use a calculator, but SHOW ALL WORK!!!)

f  x   1  x  sin x