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? 10. (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? OA. (2,-8) OB. (8,2) OC. (-2,8) D. (8,-2)

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? 10. (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? OA. (2,-8) OB. (8,2) OC. (-2,8) D. (8,-2)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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I have attached the image of the question with the diagram. This question is from the applications of trigonometry.
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70 P is a point on a straight line with position vector r = a + tb. Show that 7=a+2a-bt+ B² By completing the square, show that is a minimum for the point P for which t-a-b/B. Show that at this point OP is perpendicular to the line r= a + tb. (This proves the well-known result that the shortest distance from a point to a line is the length of the perpendicular from that point to the line.)
Plz solve within 30min min I vill definitely upvote and vill give positive feedback thank you plz quick
Plz answer both correctly asap