Question

Someone know how to isolate c from -12/(c-3)^3

Answer 1

We can't isolate the c here if there is no equation. Or we can do that when we substitute values for c.

Answer 2

here is the question @Yttrium Let f(x) = (x − 3)^−2. Find all values of c in (1, 7) such that
f(7) − f(1) = f '(c)(7 − 1).

Answer 3

any help @hartnn

Answer 4

which topic does this belong ? mean value theorem ?

Answer 5

yeah

Answer 6

could you find f'(x) first ?

Answer 7

from f'(x) you could get f'(c), by just plugging in x=c

Answer 8

isn't f'(x)=-2(x-3)^-3

Answer 9

correct,
so f'(c) = -2 (c-3)^-3

now find f(7)and f(1)
and plug those in
f(7) − f(1) = f '(c)(7 − 1).

Answer 10

I did and i got -12/(c-3)^3

Answer 11

you should get an equation...

Answer 12

For f(7)=1/16 and f(1)=1/4

Answer 13

so is the c= -3/16

Answer 14

no, f(7) and f(1) were incorrectly calculated.

Answer 15

Oww. I thougt f'(c) --> Inverse function of x wrt c. :((

Answer 16

dont you have to calculate for c?

Answer 17

to get f(7), just plug in x=7 in f(x)
'c' doesn't even come in picture to get f(7) and f(1)

Answer 18

oh okay but to calculate this part how do you do it f '(c)(7 − 1).

Answer 19

what did you get for f(7) and f(1) ?

Answer 20

together -3/16

Answer 21

what is together ?
f(7) = (x-3)^-2 at x=7
= 1/16
f(1) = 1/4
you were correct about f(7) and f(1)

so,
f(7) − f(1) = f '(c)(7 − 1) gives
1/16 -1/4 = -2(c-3)^-3 *6
just try to isolate 'c' from here

Answer 22

so,
-3/16 = -12 (c-3)^-3
1/64 = 1/(c-3)^3
gives, 64 = (c-3)^3

take cube root on both sides, what u get ?

Answer 23

is it 7

Answer 24

yep, c=7, thats correct :)

Answer 25

is there any more because when I put 7 I got it wrong

Answer 26

yes, thats because c has the range (1,7)
which means 1 and 7 are not included
so, c cannot take the value of 7

Answer 27

so it does not exist

Answer 28

yup, i would say there's no solution

Answer 29

which one would you say it is from the attach list?

Answer 30

i would have gone with b
as MVT applies for continuous functions

Answer 31

cool got them both right thank you so much hartnn!!!!!!

Answer 32

nice ! welcome ^_^