Respond with true or false; to each of the following assertions: A differentiabl

Question

Respond with true or false; to each of the following assertions: A differentiable function / of two variables has a local extreme value at (a,b) if and only if fx(n,b) = 0 and fy(a,b) - 0. If two lines in three-space are not parallel then they intersect at some point. The divergence of a vector field is a function. A vector field F is conservative if and only if div(curl F) = 0. A surface in tlnee-space can always be oriented. A saddle point, determines either a local maximum value or a local minimum value.

Explanation / Answer

a.) true

b.)false (skew lines)

c.)true (scalar function)

d.) true

e.) true

f.) false (neither max nor min also possible eg. y=x^3 at x=0)

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