Jessie just finished the probation period at work and got a $0.50 per hour raise and 4 more hours of work per week. Jessie's friend scoffed, “That's only $2 more per week! Who cares?”

Why is Jessie's friend wrong about the change in Jessie's weekly pay? What more do we need to know about Jessie's work situation to calculate the actual change in the pay?

How is this related to the product rule in calculus class?

Question

Jessie just finished the probation period at work and got a $0.50 per hour raise and 4 more hours of work per week. Jessie's friend scoffed, “That's only $2 more per week! Who cares?”

Why is Jessie's friend wrong about the change in Jessie's weekly pay? What more do we need to know about Jessie's work situation to calculate the actual change in the pay?

How is this related to the product rule in calculus class?

anonymous · Answer

The first piece of the puzzle that you would need is the amount of hours Jessie works per week. Jessie will not be making just 4 more dollars a week he would also be getting an additional 50 cents for each hour that he/she (the question is unisex :) )  works. The product rule states that the derivative of a combination of 2 or more functions is the derivative of the first times the second plus the derivative of the second times the first. In other words $$d/dx f(x)g(x) = f \prime (x) g(x) + f(x)g \prime(x)$$

anonymous · Answer

Ok that helps so much! Thank you.