Question

value thorem question: photo attached

Answer 1

@electrokid

Answer 2

(A) mean slope = \(\frac{y(b)-y(a)}{b-a}\)

Answer 3

then for (B) find \(f'(x)\) and set it equal to the above slope.
then solve for "x"

Answer 4

for mean slope, is it 1?
10-(-5)/10-(-5)?

Answer 5

I also deriviate f(x)
6x^2-18x-108

Answer 6

no , y(b) you have to evaluate.
\[f(a=-5)=2(-5)^3-9(-5)^2-108(-5)+5=?\\
f(b=10)=2(10)^3-9(10)^2-108(10)+5=?
\]

Answer 7

a=70
and
b=25?

Answer 8

you mean,
f(a)=70
and
f(b)=25

Answer 9

yes

Answer 10

then do i plug this into the equation ?

Answer 11

now, \[m=\frac{f(b)-f(a)}{b-a}\]

Answer 12

slope is 3?

Answer 13

25-70/10+5

Answer 14

@electrokid Thank you, I entered the answer and it was correct.
What is the first step for next question?

Answer 15

find f'(x)

Answer 16

6x^2-18x-108

Answer 17

F'(x)=6x^2-18x-108?

Answer 18

@electrokid please help

Answer 19

great. yes.

Answer 20

now,
set \[f'(c)=m\\
6c^2-18c-108=3\]
solve for "c"
you will get more than one value
but you have to use the value of "c" by mean value theorem, in the interval [a,b]
i.e.,
-5<c<10

Answer 21

why its 3?

Answer 22

c^2-c=(111/18)/6

Answer 23

because f'(c) should be equal to the slope

Answer 24

o.. I see.

Answer 25

no
\[6c^2-18c-111=0\]

Answer 26

use the quadratic formula

Answer 27

I go
18\[\frac{ 18pmsqrt(2340) }{ }\]

Answer 28

I got
18 (pos neg)sqrt(2340)/12

Answer 29

yep
thats the one

Answer 30

Thank you,
I got -2.531,5.531?

Answer 31

@electrokid

Answer 32

you sure?
well then both would be your answers

Answer 33

I do-not think both of them are right answers.
I entered it and it says it was wrong!

Answer 34

\[{18\pm\sqrt{(18^2-4(-111)(6)}\over12}={18\pm\sqrt{2988}\over12}
\]

Answer 35

6.055 and -36.662

Answer 36

it still tells me wrong!

Answer 37

but see...
our domain is [-5,10]
"6.055" is in domain
but
"-36.66" is not in the domain

Answer 38

O... i entered 6.055 and still tells me its wrong

Answer 39

the other number is not "-36"
it should be "-3.055" which is also in the domain

your two answers must be
6.055 and -3.055

Answer 40

it still tells me wrong