## LaddiusMaximus 4 years ago estimate instantaneous rate of change at the point x=5 for f(x)=lnx

1. amistre64

the derivative of lnx at x=5

2. amistre64

1/5 maybe?

That is not what it is asking. Im supposed to use the average velocity formula to figure it out and its not working

4. amistre64

the average velocity is for an average rate of change; your spose to be using the limit of that formula as h goes to 0 or some other denominator

I know that but we havent gotten that far. We are only using rates of change.

6. amistre64

instantaneous velocity is the derivatie; which can be defined as:$\lim_{h->0}\frac{ln(x+h)-ln(x)}{h }$

7. amistre64

then use the avg stuff with small changes

8. amistre64

ln(5)-ln(5.0001)/.0001

9. amistre64

or something akin to it

the way the book and cramster teaches it is way different. im supposed to use numbers a little more and a little less than five

like 4.9 and 5.01

12. amistre64

teh smaller the change, the more exact the estimate

(5)^3 +5-((4.9)^3 +4.9)/ 5-4.9

well it asks for estimates and all the ones I give are wrong

15. amistre64

cubed stuff?

16. amistre64

you said lnx

I end up with 68.75, 73.04,74.51,75.85

I dont know man. Ive been beating my head against the wall for the last two hours and the book is nigh on useless

19. amistre64

ln(5.00001/5)/.00001 = .2000...... approx 1/5 http://www.wolframalpha.com/input/?i=ln%285.00001%2F5%29%2F.00001

it says that the instantaneous rate of change is estimated by computing the average rate of smaller intervals

21. amistre64

thats what i did

well what am I doing then? because im lost. I dont understand how to set up the problem.

23. amistre64

ln(5.00001) is a small change from ln(5) right?

24. amistre64

in fact is .00001 small of a change

ok i follow that. but what then? how do I set up the problem to solve it? so its [5, 5.001]?

26. amistre64

yes

27. amistre64

or 4.99999 to 5 but its easier to see the change when it grows a little bigger

how do i plug it in? i see a formula for average rate of change, but it doesnt give one for instantaneous

29. amistre64

im not sure what it is youre looking at ....

30. amistre64

if its about inputing into a program, i got no idea what it wants then

31. amistre64

the instantaneous rate of change at ln(5) = 1/5 = .2

32. amistre64

so how you got those other vlaues I cant say