Find the directional derivative of f at the point (, 1) in the (V3, –1). (Hints : (a) It is faster and direction of the vector v = more convenient to use a nice theorem we proved in class. (b) v is not a unit vector.)

Consider the function f(x,y) = x² - 4y² - 9 and the point (-1,1). 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. a. What is the unit vector in the direction of steepest ascent at P? (Type exact answers, using radicals as needed.) What is the unit vector in the direction of steepest descent at P? (Type exact answers, using radicals as needed.) b. Which of the following vectors is in a direction of no change of the function at P? O A. (2,-8) OB. (8,2) OC. (-2,8) D. (8,-2)

Can you explain this question? The answer shown is correct, but I don't understand why we take the derivative to get the velocity.