a. Determine whether the Mean Value Theorem applies to the following functions on the given interval [a, b].

b. If so, find the point(s) that are guaranteed to exist by the Mean Value Theorem.

c. For those cases in which the Mean Value Theorem applies, make a sketch of the function and the line that passes through (a, f(a)) and (b, f(b)). Mark the points P at which the slope of the function equals the slope of the secant line. Then sketch the tangent line at P.

f(x) = ln 2x; [1, e]