Question

can some explain the mean value theorem to me

Answer 1

so you have an interval where you calculate average rate of change. you want to know at what point in the interval is instatanous rate of change same as average rate of change over the interval

Answer 2

If you mean lagrange's mean value theorem ,
If you have any curve f(x) between a and b such that it is both continuos and differentiable in that range, Then for some c such that a<c<b, (f(b)-f(a))/(b-a)= f'(c), basically slope of chord between a and b is equal to slope of tangent at least one point in between a and b

Answer 3

that chord is the secant line right?

Answer 4

Yes that is correct