The maximum rate of change of f at the given point and the direction in which it occurs. f(x,y)=(y^2)/x, (2,4) Answer: 4√2, <-1,1> _________________________ For this problem, since I couldn't find the upside down triangle, I am going to use delta to represent the gradient of a function. f(x,y) = (y^2)/x Δf(x,y) = <-(y^2)/(x^2), (2yx)/(x^2)> =<-(y^2)/(x^2), (2y)/(x)> Δf(2,4) =<-(4^2)/(2^2), (2*4)/(2)> =<-16/4, 4> =<-4,4> and since Δf is a vector i can divide this by the scalar 4 to get, =<-1,1> However, I have no idea on how to approach the problem when it comes to finding the maximum rate of change (which, in this problem, is 4√2). I tried finding the unit vector of Δf and multiplying it by Δf in hopes that it will give me the maximum rate of change but it didn't. Also, I found that this approach is the wrong approach, not only because it gave me the wrong answer but, because the answer this would give me would depend on whether or not I changed Δf by the scalar 4. Can somebody guide me in the right direction! I found that the direction of the maximum rate of change is the gradient of the function but to find that rate of change vexes me! Thank you for taking the time to review my problem.