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For each of the following statements, determine whether the statement is true or false. In each case, explain why your determination is correct.

  1. If $f (x,y)$ is a continuous function and $∇f (a,b) = 5$, then there is no direction from the point $(a,b)$ for which the derivative equals $-7$.

  2. A function $f(x,y)$ can have two local maxima and no local minima.

  3. If two surfaces are tangent to one another, their normal lines at the point of tangency are Perpendicular to each other.

  4. We can always change the order of integration in double integrals.

Please Correct me, 1) false 2) true 3)false (they should be parallel 4) true

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closed as not a real question by robjohn Nov 25 '12 at 18:42

It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.

Besides copy-and-pasting, what have you tried? –  The Chaz 2.0 Nov 25 '12 at 2:56
Please consider being polite and avoid just throwing your homework on people's face since we do not actually work for you. –  beauby Nov 25 '12 at 2:56
If I had any idea , I won't "Copy Pasted" them here . –  Hooman Nov 25 '12 at 3:02
so if these are your troubles try to divide your question in 4 questions and ask separately, it's better :) –  user42912 Nov 25 '12 at 3:31
The author asked that this question be deleted, but since there was an upvoted answer, I have closed it. –  robjohn Nov 25 '12 at 18:43

1 Answer 1

up vote 1 down vote accepted

Hint: Gradient vector of a function $∇f$ points in the direction of greatest rate of increase of $f(x,y)$.

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