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

1. anonymous

2. anonymous

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.

3. anonymous

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

4. anonymous

@amistre64

5. amistre64

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

6. amistre64

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

7. anonymous

What do mean by define how it applies?

8. amistre64

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

9. anonymous

The function must be continuous and differentiable

10. amistre64

..." 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

11. amistre64

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

12. amistre64

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

13. anonymous

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

14. anonymous

I could post the problem if it would help

15. amistre64

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

16. anonymous

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

17. anonymous

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

18. amistre64

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

19. anonymous

So how would I find the parallel lines?

20. amistre64

parallel lines have the same slope ....

21. anonymous

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

22. amistre64

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

23. amistre64

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

24. amistre64

this is just another wording of the MVT

25. anonymous

Okay thank you!

26. amistre64

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