Question

Determine if the Mean Value Theorem applies, then find "c" such that f'(c)=(f(b)-f(a))/(b-a)

Answer 1

f(x)=x^3-x^2-2x for [-1,1]

Answer 2

why would the answer be c=-1/3 and not 1 @TweT226

Answer 3

you have to take the derivative

Answer 4

\[f'(c)=\frac{ f(b)-f(a) }{ b-a }\]
\[3c^2-2c-2=\frac{ -2-0 }{ 1- (-1)}\]

Answer 5

\[3c^2-2c-2=-1\]
\[3c^2-2c-1=0\]
\[(3c+1)(c-1)=0 \]
\[c=\frac{ -1 }{ 3 }, 1\]

Answer 6

so how come my teacher chose \[\frac{ -1 }{ 3}\] over c=1?

Answer 7

I think it's because it's right on the endpoints

Answer 8

what do u mean

Answer 9

i mean interval [-1, 1]

Answer 10

the theorem states that the equation is differentiable between (a,b) not [a,b] the domain is [=1,1] in the problem, so when you take the derivative, c cannot equal a or b.

Answer 11

oh u mean it's in between

Answer 12

oh ok gotcha ;)

Answer 13

-1*

Answer 14

yeah

Answer 15

@yun2thejae can u help me with another problem pls? ^^

Answer 16

sure, if you would like.