Question

Problem 3. (a) Use Newton's Method with $f(x) = x^3 - 5x^2 - 2x + 8$ and initial value $x = 1$ to find one of the roots of $f(x)$ accurate to 6 decimal places. Write down your approximation at every step, and stop when the first six decimal places are no longer changing from one approximation to the next. (b) Use a graph to estimate good starting values to find the two other roots for $f(x) = x^3 - 5x^2 - 2x + 8$ using Newton's Method, and then use Newton's Method to find the roots accurate to six decimal places, writing down your approximations at each step. Problem 4. Let $f(x) = 2^x + x^2 - e$. (a) Use a graph on your calculator to find a good starting point for Newton's Method for finding the zeroes of $f(x)$. How many zeroes are there? (b) Find all zeroes of $f(x)$ accurate to 6 decimal places, writing down your approximation from Newton's Method at each step.

          Problem 3.
(a) Use Newton's Method with $f(x) = x^3 - 5x^2 - 2x + 8$ and initial value $x = 1$ to find one of the roots of
$f(x)$ accurate to 6 decimal places. Write down your approximation at every step, and stop when the
first six decimal places are no longer changing from one approximation to the next.
(b) Use a graph to estimate good starting values to find the two other roots for $f(x) = x^3 - 5x^2 - 2x + 8$
using Newton's Method, and then use Newton's Method to find the roots accurate to six decimal
places, writing down your approximations at each step.
Problem 4. Let $f(x) = 2^x + x^2 - e$.
(a) Use a graph on your calculator to find a good starting point for Newton's Method for finding the zeroes
of $f(x)$. How many zeroes are there?
(b) Find all zeroes of $f(x)$ accurate to 6 decimal places, writing down your approximation from Newton's
Method at each step.

Problem 3.
(a) Use Newton's Method with f(x) = x^3 - 5x^2 - 2x + 8 and initial value x = 1 to find one of the roots of
f(x) accurate to 6 decimal places. Write down your approximation at every step, and stop when the
first six decimal places are no longer changing from one approximation to the next.
(b) Use a graph to estimate good starting values to find the two other roots for f(x) = x^3 - 5x^2 - 2x + 8
using Newton's Method, and then use Newton's Method to find the roots accurate to six decimal
places, writing down your approximations at each step.
Problem 4. Let f(x) = 2^x + x^2 - e.
(a) Use a graph on your calculator to find a good starting point for Newton's Method for finding the zeroes
of f(x). How many zeroes are there?
(b) Find all zeroes of f(x) accurate to 6 decimal places, writing down your approximation from Newton's
Method at each step.

Added by Nancy L.

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