Question

how can I use the mean value theorem to prove that for some c, f'(c)=1

Answer 1

is this the same thing as proving the rolem theorem?

Answer 2

It's certainly similar to Rolle's Theorem (I think that's what you mean by rolem theorem). But you wouldn't be proving that. You would need to know that \(f(x)\) is continuous on some interval [a,b], and differentiable on the interval (a,b), where a and b are chosen such that \[\frac{f(b)-f(a)}{b-a}=1\]Once you've satisfied those conditions, you can use the mean value theorem to say that there must be some c such that f'(c)=1.

Answer 3

Fortunately, if this is a calc 1/2/3 class, you probably don't have to worry too much about continuity and differentiability since whatever function you're working with is probably continuous and differentiable on some obvious intervals.

Answer 4

in Rolle's theorem tangent at point c is parallel to X-axis
whereas in Mean value theorem tangent at c is parallel to the chord joining the end points in an interval.

Answer 5

I do know that its differentiable and continuous and I have an interval they gave me.

Answer 6

roles is a generalization of the mvt,

Answer 7

so should I solve for that formula?

Answer 8

hmm.. not sure what you meant @zzr0ck3r

Answer 9

Roles theorem is used to prove the MVT

Answer 10

What's the interval and function they gave you?

Answer 11

if i remember correctly ...

Answer 12

they gave me 1<=x<=3

Answer 13

and they gave me the function of the tangent line to a point.

Answer 14

but they told me to assume that its continuous

Answer 15

The function of the tangent line? But not the actual function? It doesn't happen to have a slope of 1 does it?

Answer 16

they didn't tell me the slope of the actual function. i'm assuming that i'm suppose to figure that out with derivative they gave me.

Answer 17

If both the conditions of MVT are satisfied then
\[f'(c)=\frac{ f \left( 3 \right)-f \left( 1 \right) }{3-1 }\]

Answer 18

I'm a little unsure of what information they have/haven't given to you. Could you post the information that you have? (such as any functions and what they are, intervals, etc)

Answer 19

hmmm I think I pretty much posted what was on the problem...

Answer 20

What's the function of the tangent line?