The commutator of two operators a and b is defined as [a, b] = ab-ba. a) given the operators a = a+bx and b=d/dx, calculate [a, b]f(x). b) do a and b commute?

Sometimes questions that involve graphs will ask you to consider the effect of a changing factor or factors. problem​ statement: right arrow the line labeled d1 in the graph to the right shows the number of cups of lemonade that caroline and emily can sell at their lemonade stand at various prices. caroline and emily have noticed that they sell more lemonade when​ it's hotter. click anywhere on the graph to open a window with a control labeled temperature. if you use the slider to change the​ temperature, the line will shift. change the temperature from 80 degrees to 100 degrees. ​question: right arrow at a price of​ $0.50, how many more or fewer cups of lemonade do caroline and emily sell when the temperature is 100 degrees than when the temperature is 80​ degrees? ​(note: indicate the change in cups of lemonade​ sold: fewer will be a negative number and more will be a positive​ number)