General Instructions: 1) Write your solution on a clean white-background paper. 2) images or figures necessary to support answers may be attached as pdf. 3) If solutions are handwritten, use blue or black ballpens in writing. Problems: 1. [25 points] Refer to table below to answer the following: 2017 Let x represent time (in years), with x = 0 correspondingto 200?, and let y represent the corresponding expenditures (in millions of pesos) for research and construction listed in the table (Health Care Expenditures). 3) Enter the appropriate data set in any graphing utility (ex. Rapidminer, Excel, Geogebra, Matlab, etc.) and nd a quadratic regression equation (ex. y = air2 + bx + c for the data. b) Use the quadratic regression equation to approximate (to two decimal places) the instantaneous rate of change of expenditures for research and construction with respect to time in 2019. Table : Health Care Expenditures of Department of Health Year 2017 2018 2019 2020 2021 Services and 376.9 421.2 489.6 639.1 735.4 supplies Research 15.2 18.9 20.4 22.8 24.1 and construction (note: data indicated are hypothetical and not actual data from DOH) 2. [25 points] Consider the function: f (x) = 2x3 3x2 12:: + 24- in answering the following: 3) Find the maximum and minimum points (if any) using the second derivative test. b) Find point/s of inflection (if any) c) Find the maximum and minimum value of the function on the interval [2, 1]