0
$\begingroup$

Consider w = x² - y² + 3z². At (1, 1, 1), what is the fastest rate of change for w? What is a direction along which there is no change in w?

I know how to do the first part, since the fastest rate of change is just the value of the gradient at the point. But how do I find a direction along which there is no change in w?

Would the direction be (1, 1, 0)?

$\endgroup$
0
$\begingroup$

Well, the change in the direction $v$ is always the scalar product $$ \langle \operatorname{grad} w, v\rangle = \langle (2,-2,6)^t,v\rangle $$ so your answer is correct (hint: there is another direction...)

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.