help on calc III problem with directional derivatives?

The function f(x,y,z) =x*e^y+z^2

a) calculate the gradient. (got this part should be (e^y, e^(y)*x, 2z))

Here is the confusing part:

Find the direction in which f increases most rapidly. We were not given the point, P(x,y,z) so we have to find it, could someone tell me how this is done with the information given,?

the last part c. involves fndng the directional derivative, which i know how to do, its just this intermediate step i am confused with.

Update:

the intermediate step is letter b. in the probelm.

1 Answer

Relevance
  • Anonymous
    9 years ago

    yea so e equals m times c squared and then you multiply that by 3. now you divide that by .69 and find the square root. Then you plug that into the Pythagorean theorem. if you don't know what that is its the a squared plus b squared equals c squared. plug a in as your favorite number, any number works good pull it out of a hat it doesn't matter. then b is what you got from dividing by .69 and finding the square root. now add them together and you get c squared. square root that and you will get c. take c and and multiply it by pi. that should be your answer.

    Source(s): my rectum
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