1. [4 marks] The apparent temperature of the air at a certain temperature and humidity level is known as the heat index. If i represents the relative humidity (in percent), then the heat index (in degrees Fahrenheit) for an air temperature of 100 F can be approximated by the function f(x) = 0.009x2 + 0.139r +91.875. (a) When the humidity level increases from 30% to 50%, what is the average rate of change of the heat index? Interpret your answer. (b) At what rate does the heat index change when the humidity level reaches 50%? Interpret your answer. 5. [3 marks] Find an equation of the tangent to the curve y = 23 Inx2 at (e, e3).3. [4 marks] Differentiate the following functions and simply the answers fully: (a) f(x) = evar tari (b) f(x) = (5x + 2c' + 2) (Inx)2. [6 marks) Find the derivative of the following functions using the limit definition. No points will be awarded for simply using derivative rules.) (a) f(x) = -53+2 (b) f(x) = v3-4r