question about mean value theorem

[mathhelp1a]

f(x) = x^3 - 5x^2 - 3x
find the mean value theorem to find all numbers c in the interval (1,3)

i got the answer 5 +- (sqrt 16) / 3
am i correct

 

[chrisr]

you're very nearly correct.
You appear to have made an invalid simplification after solving the quadratic for f[sup:38nfqfbl]'[/sup:38nfqfbl](x)
Check your values again during your final steps.
Remember also how c is calculated.
Correct the error and take the remaining steps to find c.

 

[chrisr]

[attachment=0:3ov0jgdl]mvt.jpg[/attachment:3ov0jgdl]

 

[mathhelp1a]

i got the answers 1, and 7/3

 

[chrisr]

can you show how you worked those out,
you still have work to do

 

[mathhelp1a]

-27- -7 / 3-1 = -10
f'x = 3x^2 - 10x - 3 = -10

3x^2 - 10 x + 7 = 0

quadratic equation

10 + - (sqrt 16) / 6

 

[chrisr]

That's it.
You should put brackets around the numerator.
Do you see why your first post needed correction?

 

[mathhelp1a]

yeah i messed up the quadratic formula
thanks!!!!!

 

[BigGlenntheHeavy]

\(\displaystyle Is \ 1 \ in \ the \ interval \ (1,3)? \ I \ don't \ think \ so, \ hence \ c \ = \ \frac{7}{3}.\)

\(\displaystyle Note: \ Brackets \ [] \ and \ parenthesis \ () \ are \ very \ important, \ especially \ for \ endpoints \ and \ the\)

\(\displaystyle proper \ use \ of \ them \ is \ the \ difference \ of \ getting \ an \ A+ \ on \ your \ test \ or \ a \ big \ fat \ goose \ egg.\)

 

[mathhelp1a]

its paranthesis so what that mean (1,3)
ohhh only 7/3 then

 

[BigGlenntheHeavy]

\(\displaystyle [1,3] \ means \ 1 \ \le \ x \ \le \ 3, \ however, \ (1,3) \ means \ 1 \ < \ x \ < \ 3\)