2) Label cach as true or false- no explanation needed: 0) The partial derivative

Question

2) Label cach as true or false- no explanation needed: 0) The partial derivatives of a function of three variables (at least, the ones which ) Clairaut's Theorem guarantees that for a function of two variables for which all ill) If you start out from some point on a smooth surface and travel along a level (iv) The partial first-order derivatives of a degree-two polynomial in two variables (v) If the discriminant, or Hessian, is zero when applying the second derivative test, exist) are themselves functions of three variables. partial derivatives of the first two orders are continuous,f y Fo curve, your directional derivative (assuming it exists) will be zero. will be of degree one. we can conclude our test point is a saddle point.

Explanation / Answer

(i) False. Because it is not true always. For example, f=xyz.

(ii) True

(iii) False. Directional Derivative may not be zero.

(iv) True

(v) False. If discriminant is zero, then higher order test must be uses.

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