Surfaces z = x² + 2y², x + y = 0 X Parameter x = 5t

a. Sketch the graph of r(t) = ti+t2j. Show that r(t) is a smooth vector-valued function but the change of parameter t = 73 produces a vector-valued function that is not smooth, yet has the same graph as r(t). b. Examine how the two vector-valued functions are traced, and see if you can explain what causes the problem.

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)