1.) values of f(t) are given in the following table:

Question

t 0 2 4 6 8 10
f(t) 137 112 88 68 49 34

a. Does this function appear to have a positive or negative first derivative? Second derivative?
* I think both derivatives are negative

b. Estimate (f prime) f^' (2) and f^' (8)

Please show work for part b so I can understand. I'm really stuck.

Answer 1

i just saw the table is messed up so the values are:
(0, 137) (2, 112) (4, 88) (6, 68) (8, 49) (10, 34)

Answer 2

it is gettin smaller each increment, first derivative is negative.

Now, the rate of decrease is 25,24,20,19,15 getting smaller, so the second derivative is positive.

Answer 3

oh ok. but wut about f^'(2). how do i find that from the table?

Answer 4

0 137

====== -25

2 112 ****** +1

====== -24

4 88 ******* +4

======= -20

6 68 ******* +1

======= -19

8 49 ********* +4

======== -15

10 34

so
dy/dx is negative
but the change of dy/dx with x is positive right down the table

Between x = 0 and x = 2, y changes -25
dy/dx = -25/2 = -12.5
between x = 2 and x = 4, y changes -24
dy/dx = -24/2 = -12
so averaging to get an instantaneous dy/dx at x = 2
I would say dy/dx = -12.25 at x = 2

go through the same routine at x = 8

Answer 5

I'm getting confused on x= 8
would you do between x=0 and x= 8, the change is
-88 and then divide that by 8 = -11
between x= 8 and x= 10, y changes -15 and then divide that by 8 to get -1.875 but then what?

Answer 6

always divide by the change in x which is always 2 in your table