i just saw the table is messed up so the values are:
(0, 137) (2, 112) (4, 88) (6, 68) (8, 49) (10, 34)
1.) values of f(t) are given in the following table:
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.
6 answers
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.
Now, the rate of decrease is 25,24,20,19,15 getting smaller, so the second derivative is positive.
oh ok. but wut about f^'(2). how do i find that from the table?
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
====== -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
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?
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?
always divide by the change in x which is always 2 in your table