help me solve these math problims

1. Let f(X) = .5X+ sin(2X), Us XS 27f a. Find f"(X) and f\"(X). b. Solve f'(x)=0. Show your work. c. Solve f"(x) = 0. Show your work. d. Graph f(X), 1"(X) andf"(X). Use different colors. e. Label the relative extremes A and the inflection points B on the graph of f(X) . Label the corresponding points A' and B on the graph of f' (X). Label the corresponding points A\" and B" on the graph of f\"(X). The normal daily maximum temperature T (in degrees Fahrenheit) for Denver, Colorado, is shown in the table below. Month Jan Feb Mar Apr May Jun Tmmmwmmmm Month Aug Sep Oct Nov Dec Temperature 88.2 85.8 76.9 66.3 52.5 44.5 a. Graph the data. b. Use your calculator to find a regression equation of the form y: a *sin(bX+ C) + d (2. Graph the regression equation and the data. How well does the regression equation fit the data? d. What is the period of the regression equation? Does it make sense? e. What is the amplitude of the regression equation? What does it mean in terms of the problem? f. Find and graph dX g. Based on the graph of the derivative, during what time does the temperature change most rapidly? Most slowly