Download AP Calculus Unit 2 You Try #8

AP Calculus
Unit 2
You Try #8
Name:_____________________
Directions: Use a Pencil, Show Your Work, and Circle Your Answers
1. Find the local linearization, L( x)  f (a)  f (a)( x  a) , of the given function at the given input value a. Use the local
linearization to predict the function’s output value at a + 1. Compare the predicted value L(a  1) with the actual function
value f (a  1) and calculate the error.
a)
f ( x)  4  x , at a = 0
c)
f ( x) 
1
1
, at a 
2
x
3. Complete five iterations of Newton’s method for the given
function using the indicated initial guess.
f ( x)  sin x  x  1 , x0 = 1
b)
f ( x)  ln x , at a = 1
2. Complete five iterations of Newton’s method for the given
function using the indicated initial guess.
f ( x )  3 x 2  2 x  4 , x0 = 1
4. Solve the equation x  ln x  2 by applying Newton’s method
to the function f ( x)  x  ln x  2 .
5. Consider the fourth degree polynomial function, f ( x)  4 x 4  12 x3  11x 2  3x .
a) Show that the zeros of f are in arithmetic
progression and find the common difference.
b) Show that the zeros of the derivative of f are also in
arithmetic progression and estimate the common difference.