I'll post what I have already solved, but I'm not sure if there's more to the question.

Question

anonymous · Answer

attachment

anonymous · Answer

f(0) = (0)^3 = 0
f(1) = (1)^3 = 1
$$\frac{ 1-0 }{ 1-0 }=\frac{1}{1}=1$$
The derivative of the function is 3x^2

3x^2 = 1
x^2= 1/3
x = sqrt(1/3)  or -sqrt(1/3)

Since only sqrt(1/3) is found in [0,1], then it is the only answer.

anonymous · Answer

Is there anything else this question is asking me to do?
(It's just worded confusingly to me)

anonymous · Answer

@amistre64

amistre64 · Answer

do you have to define how the mean value thrm applies to it?  i think it has to do with being continuous along the interval

amistre64 · Answer

other than that, you did well at finding x=c that has a slope equal to the slope between x=a and x=b

anonymous · Answer

What do mean by define how it applies?

amistre64 · Answer

what are the required conditions for the MVT to be applicable?

anonymous · Answer

The function must be continuous and differentiable

amistre64 · Answer

..." if f(x) is defined and continuous on the interval [a,b] and differentiable on (a,b)" ... http://www.sosmath.com/calculus/diff/der11/der11.html correct, and since this function is defined, continuous, and diffy-able then yada yada

amistre64 · Answer

one of the common examples of a fail for this is

f(x) = 1/x,  on the interval (-1,1)

amistre64 · Answer

a slope can be defined across the interval, but the function has no value in the interval that matches that slope ... it is not continuous or diffy-able at x=0 within the interval

anonymous · Answer

Ah okay. 
Could you interpret this by chance? ...
"Find any tangent lines to the graph of f that are parallel to the secant line."

anonymous · Answer

I could post the problem if it would help

amistre64 · Answer

more info usually helps, but the idea is to find the slope ofthe secant line in order to evaluate the derivative tha tmatches it

anonymous · Answer

Is there a formula to finding the slope of the secant line?

anonymous · Answer

Oh nevermind! It's 2/3.
I've already solved for it.

amistre64 · Answer

:)  

f(b)-f(a)
-------
   b-a

anonymous · Answer

So how would I find the parallel lines?

amistre64 · Answer

parallel lines have the same slope ....

anonymous · Answer

So it would be any function with the slope 2/3?

amistre64 · Answer

the derivative of the function (if one is given) define the slope at any single point

amistre64 · Answer

any value x=c of which f'(c) = 2/3

amistre64 · Answer

this is just another wording of the MVT

anonymous · Answer

Okay thank you!

amistre64 · Answer

youre welcome

was stuck in OS limbo for a bit :/