We might learn in a physics class that the air pressure can be found as a function of altitude h feet above sea level given by the function: P(h) = 30 e -3.23x10-s.h where P(h) is measured using inches of mercury. 6. Find the first derivative of the physics function. Show your work appropriately and simplify. 7. Find the second derivative of the physics function. Show your work appropriately and simplify. 8. Using calculus, explain how the first and second derivatives tell us whether the physics function is increasing or decreasing and whether it is concave up or concave down. 9. Now sketch a reasonable graph of P(h) = 30 e-3.23x10-5.h using the domain [0, 30000]. 3000 30 10. Sketch a reasonable graph of both the Climber's Estimate function and the physics function using the window h=[0, 5000], pressure =[25, 30]. 11. Based on your graph, for what altitudes would you suggest that the rule of thumb is sufficient in estimating air pressure? 25- 1000 2000 3000 4000 5000 Page