Exercises

1. Use Newton's Method to find all the zeros of the function in Example 2:

   `ftext[(]t text[)]=t^4-18t^2-10t+39`.

   One zero is approximately `1.27`.

2. Use Newton's Method to find all three solutions of the equation `3x^2=e^x .`
3. Use Newton's Method to find the root of `t^2-e^(-3t)=0`.
4. Let `ftext[(]t text[)]=t^3+8t^2+t-6`. Use Newton's Method to find all zeros of `f`.

Figure E1  Graph of f(t) = t³ + 8t² + t - 6
5. Let `ftext[(]t text[)]=e^t+e^(-t)-2t^2.
   1. Find the four zeros of `f`.
   2. Find the three zeros of `f'`.
   3. Find the smallest value of `f` and the two values of `t` where `f` has its smallest value.
   4. Find the largest value of `f` between `t=-1` and `t=1`.
6. Use Newton's Method to find (approximately) one solution of each of the following equations.

   a.   `x^3+5x=10`	b.   `x^3+5x=e^x`	c.   `x^3+5x=-e^x`
   d.   `x^3-5x=10`	e.   `x^3-5x=e^x`	f.   `x^3-5x=-e^x`

7. Let `ftext[(]t text[)]=t^4-10t^2+e^(2t)`. Find one zero of `ftext[(]t text[)]`.