Given that y = 3sin(theta)/(2sin(theta) + 2cos(theta)), -pi/4 < theta < 3pi/4, show that dy/dtheta = A/(1 + sin(2theta)), -pi/4 < theta < 3pi/4, where A is a rational constant to be found. (5)

The function f is defined by f(x) = e^(3x)/(4x^2 + k) where k is a positive constant. (a) Show that f'(x) = (12x^2 - 8x + 3k)g(x) where g(x) is a function to be found. (3) Given that the curve with equation y = f(x) has at least one stationary point, (b) find the range of possible values of k. (3)