Consider the function Upper F (x comma y )equalse Superscript negative x squared divided by 6 minus y squared divided by 6 and the point Upper P (negative 3 comma 3 ). a. Find the unit vectors that give the direction of steepest ascent and steepest descent at P. b. Find a vector that points in a direction of no change in the function at P.

a.

(ascent)

 (descent)

b.

Step-by-step explanation:

a. The function is given by:

the point is P(-3,3)

a. The unit vector that gives the direction of the steepest ascent is necessary to compute the gradient of F(x,y):

The, it is necessary to evaluate in the point P, and to compute the norm of the vector in order to get the unit vector:

  (ascent)

for the steepest descend you have

b.

the vector with the direction of no change is a vector perpendicular to grad(F):

furthermore, v is an unit vector:

then, the vector is:

the answer is 31.27mph