Question

Is the instantaneous rate of change of f at x=4 greater than the rate of change at x=6? Justify.

Answer 1

do I use x=2 and x=6 to determine instantaneous rate of change of f at x=4?

Answer 2

that will give you the average rate of change

Answer 3

ok, now I really don't know what to do since it states rate of change at x=6 (second part)

Answer 4

then I can use x=2 and x=4 for instantaneous rate of change of f at x=4 or I can use x=4 and x=6

Answer 5

I guess the best thing you can do is average the two average rates of change around x = 4 to get an approximation of the instantaneous rate of change

Answer 6

really, I don't think I have seen that done on AP calculus but I could be wrong

Answer 7

me neither, but idk what else to do

you're given a discrete data set when you should be given a continuous function

Answer 8

If a function is differentiable then it is continuous, correct?
My instructions above the table state:
Consider the values of a differentiable function, f(x), is the table below to answer the questions that follow.

Answer 9

that is true, but you need to be able to get very very close to x = 4 to get the instantaneous rate of change at x = 4

Answer 10

so the best you can do is do an approximation

Answer 11

ok, how about the part of "the rate of change at x=6"? what do you suppose they mean by that?

Answer 12

maybe this is just a bad worksheet.......

Answer 13

here's what I get when I plot the points

Answer 14

I guess I am trying to figure out the purpose of this worksheet. It is not flowing for me.....

Answer 15

I think what you need to do is find these two slopes

BC & CD

then average those two slopes to get the approximate instantaneous rate of change

Answer 16

maybe I should just trash this worksheet

Answer 17

ok maybe the second page is not so bad, care to see if it makes sense with me

Answer 18

Consider f(x), does Rolle's Theorem apply on the following interval? [2,14] and [2,8] Explain why or why not

Answer 19

I know that Rolle's Theorem basically states that that the instantaneous rate of change is zero. (ie horizontal tangent) or f ' (x)=0

Answer 20

it's basically a very specialized case of the MVT

Answer 21

I am sure I did not do a good job of summarizing Rolle's Theorem....

Answer 22

it says that if f(x) is continuous on [a,b] and differentiable on (a,b) AND also f(a) = f(b), then there's a value c such that f ' (c) = 0

Answer 23

so for [2,14], I put yes because f ' (c)=0 at c=8 in this case also, because I could show that f(14)=f(c)=5

Answer 24

example