Question

HELPPP!!!
Find a point c satisfying the conclusion of the MVT
for the following function and interval (Round your answer to three decimal places.) f(x) = x^−3, [1, 3]
i've gotten that (-8/9)/2

Answer 1

whats the slope from 1 to 3?

Answer 2

umm... It doesn't give that I don't think

Answer 3

this for integration or derivatives

Answer 4

oh is it -3/c^4

Answer 5

depends; what is the application of the MVT in this case?

Answer 6

that is it, because the example problem has that to the left, its like this -2/c^3 = f ' (c) = f(b)- f(a) / b-a

Answer 7

ok, then its the derivative one

Answer 8

so this one would be -3/c^4 = f ' (c) = f(b)-f(a)/ b-a

Answer 9

whats the slope of the line from 1 to 3?

Answer 10

idk im guessing it is -3/c^4 the derivate of x^-3 with f '(c)

Answer 11

\[slope =\frac{f(3)-f(1)}{3-1}\]

Answer 12

the change in y over the change in x

Answer 13

oh it is (-8/9) / 2

Answer 14

\[\cfrac{\frac{1}{27}-\frac{1}{1}}{2}=\cfrac{\frac{1-27}{27}}{2}=\frac{-26/27}{2/1}=-13/27\]

Answer 15

so, at what point "c" is the derivative equal to -13/27

Answer 16

ahh dang, i see, and then you somehow plug that into -3/c^4 im guessing?

Answer 17

yes, you then equate that slope with the derivative at "c"

Answer 18

\[\frac{-3}{c^4}=\frac{-13}{27}\]

Answer 19

-13/-9 = c^4

Answer 20

wait -9/13 = c^4

Answer 21

\[\frac{-3(27)}{-13}=c^4\to \color{#ff0080} {c=\sqrt[4]{\frac{-3(27)}{-13}}}\]

Answer 22

holy crap haha, now the question is what is that in decimal form

Answer 23

whatever the calculator gives you :)

Answer 24

c=(-3(27/(-13)))^(1/4)

Answer 25

http://www.wolframalpha.com/input/?i=%28-3%2827%2F%28-13%29%29%29%5E%281%2F4%29

Answer 26

my calculator gae me 1.580

Answer 27

yep

Answer 28

thanks!!

Answer 29

yw

Answer 30

1/2 c ^-1/2 = 1/9 is that the same as 1/c^2 = 1/9

Answer 31

\[\frac{\sqrt{c}}{2}\ne c^{-2} \text{ in general}\]

Answer 32

y = \[\sqrt{x}\]

Answer 33

so c would equal something weird

Answer 34

i dont know, depends on what you are trying to do ...

Answer 35

the derivative of the square root of x = 1/9

Answer 36

(4x)^{-1/2} = 9^{-1}

hmmm

Answer 37

((4x)^{-1/2} = 9^{-1} )^{-2}

4x = 9^2

x = 81/4

Answer 38

maybe

Answer 39

yeah, thats good lol

Answer 40

so you did 1/2 (x) ^-1/2 = 2*2x ^-1/2 = 1/9
so 9^-1 = 4x^-1/2 so then you square 9 and divide by 4

Answer 41

i did yes; but its simpler than that really :)

\[2\sqrt{x}=9\]
\[\sqrt{x}=9/2\]
\[x=81/4\]

Answer 42

oh okay gotcha (: i need help with another one, it involves sin and cosine

Answer 43

<---- post it to the left

Answer 44

okayyy