use h = 0.001

Table 1

 

f(x)2	2f(x)k(x)
(ax + b) 2	(Example) 2(ax + b)(a)
(ax2 + bx + c) 2
(ax3 + bx2 + cx + d) 2

 

Table 2

 

n	Value of nf(x)n– 1 at x = -1	Approx value of  at x = -1	Value of f ' (-1)
2	2((-1)^2 -3(-1)) = 8	(f(-1+.001)^2-f(-1)^2) / .001 = - 39.967	-5
3
-1
1/2

 

Table 3

 

sin(f(x))	cos(f(3))	f’(sin(f(x)) at x=3	f’(3)
sin(2x)	.96017	1.92090	2
Sin(x/2 + 3)
sin(x2)
sin(ex)

 

After the Lab (10 pts – 1 pt per question)

 

1. (a)  In Table 1, what relationship does the function k(x) bear to the original function 

          f(x)?

           

           

 

    (b) After you figure out their relationship, write down the resulting rule from Table 1:

             (f( x)) ² =

 

    (c) Without using Derive, use your rule above to find

            (6x³ + 2x² – 7) ² at x = 8. (Show all work)

 

 

 

 

 

 

           

2.  (a) In Table 2, pick a row and look at the numbers in each column. What is the 

           relationship between the three columns you filled in? After analyzing data you 

           should be able to come up with a rule that works for all the four rows.

 

 

 

     (b) Write down the resulting rule from Table 2: ( Here I want you to write down a 

           some sort of expression , rather than numbers from table 2. All you need to write 

          down this expression can be found in the first row of  table 2)

 

          (f( x) ⁿ) =

 

      (c) Without using Derive, use your rule above to find

 

              (x³ – 2x² – 2x + 6) ³ at x = –4. (Show all work)

           

3. (a) In Table 3, what is the relationship between the three columns you filled in?

 

           

           

    (b) Write down the resulting rule from Table 3. (similar to question 2)

 

         sin (f(x)) =

 

    (c ) Without using Derive, use your rule above to find

 

          sin (x²) at x = π.( Show all work )

 

 

 

 

 

 

 

            4. Combine rules 1-3 above:

     g( f( x)) =