anonymous
  • anonymous
Graph the function f(x)=x^3−2x and it's secant line through the points (-2,-4) and (2,4). Use the graph to estimate the x-coordinate of the points where the tangent line is parallel to the secant line. Find the exact value of the numbers c that satisfy the conclusion of the mean value theorem for the interval [-2,2].
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
I need help finding 'c'
anonymous
  • anonymous
I know that the Mean Value Theorem says... \[\frac{ f(b)-f(a) }{ b-a }=f'(c)\]
anonymous
  • anonymous
just apply that...

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
But that gives me f'(c)
anonymous
  • anonymous
lemme check
anonymous
  • anonymous
here a=-2 b=2
anonymous
  • anonymous
Right, plugging all that in do you get f'(c) = 2 ?
anonymous
  • anonymous
i get 8
anonymous
  • anonymous
How?
anonymous
  • anonymous
f(b)=2^3-2(2)..rite?
anonymous
  • anonymous
f(a)=(-2)^3-2(-2)
anonymous
  • anonymous
Doesn't it already give us the coordinates for the points? (2,4) and (-2,-4)
anonymous
  • anonymous
Is it wrong to say \[\frac{ 4+4 }{ 2+2}=\frac{ 8 }{ 4 } = 2\] ? Or am I totally wrong right now? Lol
anonymous
  • anonymous
what did u do just now?
myininaya
  • myininaya
\[(x^3-2x)'|_{x=c}=\frac{f(2)-f(-2)}{2-(-2)} \\ (x^3-2x)'|_{x=c}=\frac{4-(-4)}{2-(-2)} \\ (x^3-2x)'|_{x=c}=\frac{4+4}{2+2}\] that is right for the right hand side
anonymous
  • anonymous
Well I plugged in f(a) = -4, f(b) = 4, and a=-2, b=2 in the mean value theorem formula
anonymous
  • anonymous
what happens to the left hand side?
anonymous
  • anonymous
do i just derive it?
myininaya
  • myininaya
you still have to differentiate the left hand side and plug in c afterwards as the equation above suggests
anonymous
  • anonymous
3x^2 - 2 right?
myininaya
  • myininaya
yep and plug in c (though that part doesn't matter to much; it is just what they call it in the formula above) yep now solve 3x^2-2=2
myininaya
  • myininaya
or you named it c 3c^2-2=2
anonymous
  • anonymous
Ohh so then its +/- 2/sqrt3 right?
myininaya
  • myininaya
are both of those in the given interval?
anonymous
  • anonymous
hmmm... yes?
myininaya
  • myininaya
ok then cool stuff
anonymous
  • anonymous
Thats it? :O
myininaya
  • myininaya
that is it
myininaya
  • myininaya
though there are two problems
myininaya
  • myininaya
did you do the first problem?
anonymous
  • anonymous
Yay!!! Thats correct! :D Thank you so much!
myininaya
  • myininaya
we did the second problem we found the exact solutions
anonymous
  • anonymous
Yeah Im always better in graphing haha
myininaya
  • myininaya
alright
anonymous
  • anonymous
Thanks again for the help! :)
myininaya
  • myininaya
np
anonymous
  • anonymous
tracy?got the answer for the second part?
anonymous
  • anonymous
Yeah! I got it, its + or - 2/sqrt3
anonymous
  • anonymous
Thank you too @chethus!

Looking for something else?

Not the answer you are looking for? Search for more explanations.