Directional derivative, and max rate of change and direction

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Directional derivative, and max rate of change and direction

Stuck on this problemGiven the functionf(x,y)=ln(2x²+3y²)a) Find the directional derivative at (1,2) in the directionv=2i+3jb) Find the maximum rate of change and of f at the given pointand the direction at which it occurs.

math calculus

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Answer 1

Answer #1

Thank you so much, I figured out how to do thie first part but our teacher never went over the second part, your a huge help thank you so much again! :)

answered by: Catina

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Answer 2

Answer #2

You have the function

a) This part is asking you to find the directional derivativeof

at

inthe direction of thevector

.Firstcompute the gradient as follows:

Now compute the gradient at the specified point:

Because you need a unit vector

tocompute the directional derivative,you will need to normalize thegiven vector

as follows:

By definition, the directional derivative is given by

So your directional derivative will be:

(ANSWER)b) A unit vector in the direction in which

changesmost rapidlyat

willbe:

(ANSWER)The maximum rate of increase at

willbe

(ANSWER)Jon AKA THE BIG UNIT

answered by: randydemerchant

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Answer 3

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Directional derivative, and max rate of change and direction

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