A team of students seeks to make a flag representing their commitment to the earth. They will be using a green triangle inscribed in a yellow semi-circle with a radius of 40 cm. The base of the triangle will have a width of x and the midpoint of the base will be at the centre of the circle. The function to represent the area of the triangle with relationship to the base is A (x) = 12 V6400 - 2 a) Determine a simplified representation for the derivative of A(x). (3 marks) b) Use your knowledge of derivatives to determine the maximum area of the triangle