Let f be a function of two variables that has continuous partial derivatives and consider the points A(1, 4), B(12, 4), C(1, 11), and D(13, 20). The directional derivative of f at A in the direction of the vector AB is 3 and the directional derivative at A in the direction of AC is 15. Find the directional derivative of f at A in the direction of the vector AD. (Round your answer to two decimal places.)

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis. 3- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in part b?