It consists of two parts and both are compulsory. (K5, T5, A5, C5) Part1: Investigate, using graphing technology, (such as graphical calculator or DESMOS) connections between key properties such as increasing/ decreasing intervals, local maxima and local minima, points of inflection and intervals of concavity, of the function F(x)= x³ + 2x²-3x And the graphs of their first and second derivatives. Show each step in progressive manner. Part 2: The size of a population of butterflies is given by the function 6000 P(t) = where t is the time in days. 1+49(0.6) Determine the rate of growth in the population after 5 days using derivative, and verify graphically using technology.