Question

Tangent line question

Answer 1

Show that the function has at least one zero on the interval. (using the Intermediate Value Theorem)
\[f(x) = \frac{ x^2-2x }{ 3x+1 } [1,5] \] f(c) = 3/10

Answer 2

So... so far, I plugged 1 into the original equation and 5 as well. That got me -1/4 and 15/16

Then I tried plugging 3/10 in... got some weird stuff.. what should I do next??

Answer 3

f(c)=3/10 was given to you?
I don't understand what that has to do with the problem 0_o

Answer 4

I don't either :/ haha. hmmm

Answer 5

f(1) = negative number
f(5) = positive number

And f(x) is continuous on [1,5],
therefore by IVT, there is some value c in between 1 and 5 where the function crosses 0 there.

Answer 6

Oh wait wait wait.
Is this maybe about the `Mean Value Theorem`?

Answer 7

Err no I guess it wouldn't be.
Just that f(c) business confused me :P

Answer 8

So, I had a question on a test that I missed with the IVT. My teacher gave me this problem and said "same instructions".
Maybe the f(c) was a mistake... irdk