Calc III direction derivative problem

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eight10

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In what direction from the point (1, -1) is the instantaneous rate of change of F(x,y)=2x^2 - 2xy - 3y^2 equal to 2? In what direction from (1, -1) does this function increase most rapidly? What is this most rapid rate of change?


Thank you ahead of time. I imagine you want to parameterize the directional derivative somehow but i cant make it work.
 
eight10 said:
In what direction from the point (1, -1) is the instantaneous rate of change of F(x,y)=2x^2 - 2xy - 3y^2 equal to 2? In what direction from (1, -1) does this function increase most rapidly? What is this most rapid rate of change?


Thank you ahead of time. I imagine you want to parameterize the directional derivative somehow but i cant make it work.
Click to expand...

Do you know the relationship between the gradient of a function and its directional derivative and the normal plane?for a quick review - go to:

http://www-math.mit.edu/18.013A/HTML/ch ... ion06.html

Please show us your work, indicating exactly where you are stuck - so that we know where to begin to help you.
 
im stuck at the start, not sure how the gradient relates to anything. Thank you.
 
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