(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

2. Relevant equations

..

3. The attempt at a solution

We find [itex]\nabla f(1,2)[/itex] at point P: the answer is [itex](-4, 13)[/itex]. Now, we know that the directional derivative of f is given by: [itex]\nabla f(1, 2) |u| \cos\theta[/itex]

where [itex]|u| = 1[/itex] and [itex]\cos\theta=1[/itex] (since the direction is maximized at [itex]\theta\ = 0[/itex] or [itex]\cos\theta=1[/itex])

So, letting [itex]u[/itex] be the direction of maximum increase:

[itex]u =[/itex] [itex]\frac {(-4, 13)}{\sqrt{185}}[/itex]

Is that true (for the first part)? And how can I start with the second? Any help is appreciated. Oh, and [itex]u[/itex] in the first part is irrelevant of the [itex]u[/itex] in the second part of the question.

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# Direction of maximum increase and rate of change

Can you offer guidance or do you also need help?

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