The reason for this post is that I'm asking for a clarification on directional derivatives (DD). I have been doing problems involving DD to understand the concept of DD. I understand the procedure in calculating them and it seems to be pretty straight forward. the confusion arises where I have been solving DD graphcally for verification as well as mathematicallly. I have a 3D graphing system where I am able to graph the given function and also the 3D lines and planes needed to get an end result, which is the tangent to the function at a given point to find out the slope of the tangent. The answer I get, when doing it mathematically, is not consistent with what the graph is telling me. On the graph it shows a different slope from what the calculated slope gives. I know the calculated slope is correct. I've triple checked my work on the graph and all the info is correct to what is stated in the problem. I've worked three different problems and they all show inconsistencies between the calculations and what shows up on the graph. Am I reading the graph incorrectly or is the graphing system at fault? I'm not expecting a lot of answers, but if maybe someone could help explain this, it would sure help. I wish I could somehow show you an example of a problem, but I don't know how to include the graph in the post. Thanks.
Without actually seeing what you've done, there is no way at all we can know this. Software bugs, human error, almost literally anything could be going wrong with what you're doing, without actually seeing what's going wrong it's literally impossible to have anything related to an idea of what's wrong. Apologies, but this is probably not the place to ask a question like this, we can help with mathematical things which we also have sufficient information to deal with, but this problem doesn't even have one of those criteria. Best of luck.