Determine if the following are True or False. (a) If f(x,y) has a horizontal tan

Question

Determine if the following are True or False. (a) If f(x,y) has a horizontal tangent plane at (3,4), then the function f(x, y) has either a local maximum or a local minimum at (3, 4). (b) Let r(t) be a vector function. Then the unit tangent vector T(t) is equal to B(t) x N(t). (c) Let f(x, y) be a function defined over R^2. If f(x,y) has a local maximum at (-1,1), then (-1,1) is a critical point. (d) Let f(x,y) = x^2-3x-y^3+3y^2+10. Then f has a saddle point at (0,1). (e) If r(t) is a unit vector for all t, then T(t) is orthogonal to r(t) at any t.

Explanation / Answer

A true (b) false (c) true (d)true (e)true

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