Mistake

Hi gerrytrevis,

I took a look at the article that you linked to, and I believe the current version of the question is correct.

For this problem, k(t) represents the amount of ketchup produced, not the rate of ketchup being produced. Thus, k'(t) represents the rate at which ketchup is produced. So, taking the definite integral of k'(t) provides the amount produced in 4 hours, effectively undoing the derivative operation.

In the previous examples, the integral has the function r(t), which represents a rate function, not an amount function. Whereas in this example, the given function is an amount function, so you need to take the derivative first to get the rate function.

I hope this helps!