Sketch graph of the function f (x ) ~ ex X+1 Q 1 whose derivatives are: F ' ( x ) = ( xtiz ex f" ( x ) = 2 2 + 1 ex ( x + 1 1 3 specify the domain, the intercepts, the vertical and horizontal asymptotes ( if any), the local max and min ( if any), and the inflection points (if any) show all steps (hint: you can use lim ex 4-700 * + 1 = 00 ) The barometric formula gives the atmospheric pressure I as Q2 a function of the altitude h above sea level: P= Ppe- kh where K is some constant and Po is the reference pressure at sea level. Julia is running up a mountain ther watch measures that the pressure is decreasing at a constant rate of 5 k Palh. How fast is she climbing (in m/h) when she reaches h= 2000m? ( For simplicity you can assume that Po = 100k Pa and K = 10000m, which are fairly realistic values ) In Canada we are familiar with cracked windshields. cracks in windshields often appear when there is a rapid change of Qs temperature over the surface. Let's suppose that the window of a Subaru will crack if the rate of the change of the temperature in the windshield exceeds 0. 5 0C1 cm. While defrosting our windshield on a cold winter day, the bottom of the windshield quickly reaches a temperature of 10 C. Assuming the top of the windshield, located 40cm above, remains at a temperature of - 20 C should we expect cracks to develop? Justify your answer using Mean Value Theorem. ( You can assume that the temperature distribution across the windshield is continuous and differentiable ! )