Consider the function f (x comma y )equals3 x squared minus 2 y squared minus 3 and the point (negative 2 comma 1 ). 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.

see description

Step-by-step explanation:

given the function

we calculate the gradient

for each term we consider all variables different to the one we are derivating as constants. For each term we have

Therefore:

gives the direction of maxium increase.

a) with x = -2, y= 1

which magnitude is

so the unitary vector in the direction of the steepest ascent is  

and the unitary vector in the direction of steepest descent is

finally, the vector in no change direction is basically doing one of the following possibilities with :

if we have a vector <a,b> the perpendicular vector (direction of no change) will be either <-a,b> or <a,-b>

so i will select <-a,b>