Derivatives of Exponential, Logarithmic and Trigonometric Functions

The following diagram shows the graphs of \(f(x) = \ln{(3x - 2)} + 1\) and \(g(x) = -4 \cos{(0.5x)} + 2\) for \(1 \leq x \leq 10\).

1. Let \(A\) be the area of the region enclosed by the curves of \(f\) and \(g\).
   1. Find an expression for \(A\).
   2. Calculate the value of \(A\).
2. 1. Find \(f'(x)\).
   2. Find \(g'(x)\).
3. There are two values of \(x\) for which the gradient of \(f\) is equal to the gradient of \(g\), Find both these values of \(x\).