A question about mean value theorem

[m.medhat]

Homework Statement

hello ,
if f(x) is a function which satisfies the mean value theorem , where :-
$$f(x) = \left\{ {\begin{array}{*{20}c}<br /> {2x^3 - x + 1\quad \quad x \in [0,1]} \\<br /> {3x^2 - x\quad \quad \quad x \in (1,3]} \\<br /> \end{array}} \right.$$

find the value of (c) by using the mean value theorem , where (c) is the points in which the slope of tangent is equal to the slope of chord .
I want the steps of the solution please .

Homework Equations

The Attempt at a Solution

i solve with some method and find that c=13/9
and I solve with other method and find that c=2 or c=1/(sqrt 3)



very thanks >>

 

[cyby]

What method did you try to solve it with? How did you come up with those two solutions? Please show us what you've done...

 

[Quinzio]

It is not forbidden that in more than 1 point they have the same slope.